scholarly journals Boolean lattices in finite alternating and symmetric groups

2020 ◽  
Vol 8 ◽  
Author(s):  
Andrea Lucchini ◽  
Mariapia Moscatiello ◽  
Sebastien Palcoux ◽  
Pablo Spiga
Keyword(s):  
Symmetric Group ◽  
Symmetric Groups ◽  
The Other ◽  
Different Types ◽  
Boolean Lattices ◽  
Product Structures ◽  
Alternating And Symmetric Groups ◽  
Regular Partitions ◽  
Lattice Of Subgroups

Abstract Given a group G and a subgroup H, we let $\mathcal {O}_G(H)$ denote the lattice of subgroups of G containing H. This article provides a classification of the subgroups H of G such that $\mathcal {O}_{G}(H)$ is Boolean of rank at least $3$ when G is a finite alternating or symmetric group. Besides some sporadic examples and some twisted versions, there are two different types of such lattices. One type arises by taking stabilisers of chains of regular partitions, and the other arises by taking stabilisers of chains of regular product structures. As an application, we prove in this case a conjecture on Boolean overgroup lattices related to the dual Ore’s theorem and to a problem of Kenneth Brown.

scholarly journals Rhetorical questions as aggressive, friendly or sarcastic/ironical questions with imposed answers

ExELL ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 68-82
Author(s):  
Džemal Špago
Keyword(s):  
Common Ground ◽  
Peer To Peer ◽  
The Other ◽  
Communication Style ◽  
Communication Styles ◽  
Social Standing ◽  
Frequency Of Use ◽  
Different Types ◽  
Rhetorical Questions

AbstractRhetorical questions (RQs), as a cross-breed of questions and statements, represent an effective tool in putting forward the Speaker’s ideas, as well as influencing the ideas and opinions of other people. Because of their communicative effectiveness and multifunctionality, they are frequently used in different contexts and for different purposes, and, as such, they represent an interesting topic for further research. The aim of this paper is threefold: (i) to explore the nature of the implied answer to RQs, (ii) to offer a classification of RQs based on the Speaker’s communication style, and (iii) to examine whether (or to what extent) the Speaker-Addressee relationship (peer-to-peer, superior-to-inferior, inferior-to-superior) influences the selection and frequency of use of different types of RQs. Using Stalnaker’s (2002) model of Common Ground and Caponigro and Sprouse’s (2007) concepts of Speaker’s and Addressee’s Beliefs, the author redefines the nature of the answers implied by RQs, claiming that they are imposed on the Addressee rather than mutually recognized as obvious. Based on the model of communication styles as defined by Yuan et al. (2018), RQs are classified into aggressive, friendly and sarcastic/ironical questions with imposed answers. The analysis of the corpus, which consisted of 275 RQs taken from ten American movie scripts, showed that friendly RQs are more common than the other two types, and that, in instances where one of the interlocutors is in a superior position, superior-to-inferior RQs are by far more common than vice versa. The finding that RQs asked by inferiors make up less than a third of RQs occurring between interlocutors with different social standing is in line with the view that answers to RQs are imposed on Addressees.

Portals Then and Now

2009 ◽  
Vol 1 (4) ◽  
pp. 21-33 ◽  
Author(s):  
Arthur Tatnall ◽  
Stephen Burgess
Keyword(s):  
Developing Countries ◽  
Data Collection ◽  
Initial Data ◽  
Case Studies ◽  
The Other ◽  
Web Portals ◽  
Web Portal ◽  
Different Types

This article investigates the evolution of two different types of Web portals, one in Bangladesh and the other in Australia. The initial data collection was conducted in the early 2000s and revisited in 2009. The idea of a Web portal is not new, but in the last few years the portal concept has gained considerably in importance as new types of portal are developed and new uses found for portal technology. The article begins with a brief classification of the types of portals in use today and then considers some of the advantages conferred on a business in using portal technology. Developed and developing countries have different problems in making use of e-commerce and see the advantages and problems of using portals rather differently. In the article the authors examine and compare case studies of a Horizontal B-B Industry Portal in Melbourne, Australia, and a Vertical Industry Portal in Dhaka, Bangladesh.

Rational permutation groups containing a full cycle

2013 ◽  
Vol 63 (6) ◽  
Author(s):  
Temha Erkoç ◽  
Utku Yilmaztürk
Keyword(s):  
Symmetric Group ◽  
Proper Subgroup ◽  
Symmetric Groups ◽  
Transitive Permutation Group ◽  
Rational Group ◽  
Prime Degree ◽  
A Finite Group ◽  
Rational Groups ◽  
Complex Characters

AbstractA finite group whose irreducible complex characters are rational valued is called a rational group. Thus, G is a rational group if and only if N G(〈x〉)/C G(〈x〉) ≌ Aut(〈x〉) for every x ∈ G. For example, all symmetric groups and their Sylow 2-subgroups are rational groups. Structure of rational groups have been studied extensively, but the general classification of rational groups has not been able to be done up to now. In this paper, we show that a full symmetric group of prime degree does not have any rational transitive proper subgroup and that a rational doubly transitive permutation group containing a full cycle is the full symmetric group. We also obtain several results related to the study of rational groups.

scholarly journals THE CULTIVATION OF TRICHOMONAS OF THE HUMAN MOUTH (TETRATRICHOMONAS HOMINIS)

1917 ◽  
Vol 25 (2) ◽  
pp. 341-347 ◽  
Author(s):  
Tokuzo Ohira ◽  
Hideyo Noguchi
Keyword(s):  
Cultural Studies ◽  
Cell Body ◽  
Trichomonas Vaginalis ◽  
The Body ◽  
The Other ◽  
Other Hand ◽  
Deep Groove ◽  
Different Types ◽  
The Difference

Trichomonades from the mouth were studied by Steinberg who proposed to group them into three distinct types; namely, Trichomonas elongata, Trichomonas caudata, and Trichomonas flagellata. Doflein (3) regards them as probably identical with Trichomonas hominis. Opinions differ as to whether or not Trichomonas vaginalis Donné and Trichomonas hominis Grassi are the same species. Lynch, for instance, believes that they are the same species, while von Prowazek (4), Bensen (5), and others (6, 7) insist that they are different types. Bensen's view seems to be well supported by the difference alleged to be found between the mode of encystment in the two trichomonades, were it not for the fact that our knowledge about the so called cyst of trichomonades is still obscure. According to Alexeieff (8) many of the so called cysts were evidently blastomyces contained in the cell body of the trichomonas. An autogamy alleged to take place in cysts as described by Bohne and von Prowazek (9) has not been confirmed by Dobell (10). And Wenyon (11) contends that it has never been found possible to produce any development of these cysts outside the body on the warm stage as can be done with the cysts of Entamœba coli. Therefore, it is still premature to take the process of encystment into consideration as far as the classification of trichomonas is concerned. On the other hand, Rodenwaldt (12) seems to think that there are many species of trichomonas in the human intestines, and Wenyon has described a new trichomonas from the human intestines (Macrostoma mesnili Wenyon). Further cultural studies in the morphology and biology of these organisms must be carried out in order to solve these problems. In the light of modern investigations there are five subgenera to be included under the genus Trichomonas Donné. They are as follows: (1) Protrichomonas Alexeieff, with three anterior flagella, without an undulating membrane. (2) Trichomastix Biitschli) with three anterior flagella and a trailing flagellum (Schleppgeissel) without an undulating membrane. (3) Trichomonas Donné, with three anterior flagella and an undulating membrane. (4) Macrostoma Alexeieff, Amend, Wenyon (11), with three anterior flagella and an undulating membrane wedged in a deep groove (peristome). (5) Tetratrichomonas Parisi (13), with four anterior flagella and an undulating membrane. As far as our culture trichomonas from the human mouth is concerned, it has been shown that it is not strictly a trichomonas and that it should be classed under the subgenus Tetratrichomonas.

scholarly journals On alternating and symmetric groups which are quasi OD-characterizable

2017 ◽  
Vol 16 (04) ◽  
pp. 1750065 ◽  
Author(s):  
Ali Reza Moghaddamfar
Keyword(s):  
Finite Group ◽  
Symmetric Group ◽  
Prime Graph ◽  
Symmetric Groups ◽  
Degree Pattern ◽  
Alternating And Symmetric Groups ◽  
A Finite Group

Let [Formula: see text] be the prime graph associated with a finite group [Formula: see text] and [Formula: see text] be the degree pattern of [Formula: see text]. A finite group [Formula: see text] is said to be [Formula: see text]-fold [Formula: see text]-characterizable if there exist exactly [Formula: see text] nonisomorphic groups [Formula: see text] such that [Formula: see text] and [Formula: see text]. The purpose of this paper is two-fold. First, it shows that the symmetric group [Formula: see text] is [Formula: see text]-fold [Formula: see text]-charaterizable. Second, it shows that there exist many infinite families of alternating and symmetric groups, [Formula: see text] and [Formula: see text], which are [Formula: see text]-fold [Formula: see text]-characterizable with [Formula: see text].

scholarly journals Curriculum Development and Dermatology Training

2017 ◽  
Vol 15 (1) ◽  
pp. 5-11
Author(s):  
Jayadev Betkerur
Keyword(s):  
Faculty Development ◽  
Curriculum Development ◽  
Postgraduate Training ◽  
The Other ◽  
Knowledge Based ◽  
Different Types ◽  
Classification Of Diseases ◽  
Competency Based ◽  
Cosmetic Dermatology

Curriculum is an integral part of any educational cycle. Curriculum development is a systematic process involving designing, implementing , evaluating and redesigning. There are different types of curriculums being practiced by institutions. Subject based curriculum is a widely used but competency based curriculum is the best. There is an urgent need to have relook at the existing curriculum as it is beset with many problems. The  faculty development (FD) is one factor affecting curriculum development. We need to identify the other issues and address them. Presently Dermatology postgraduate training is more concentrated in imparting more knowledge based learning. Acquiring and assessing skills not included in the program.The curriculum is decades old and does not address the present needs. The classification of diseases can be modified. Evaluation methods have to be structured to assess knowledge and skill. Dermatosurgery, dermatotherapeutics and cosmetic dermatology needs to be added to the curriculum. The teachers , institutions and regulatory authorities to plan strategies to bring about these changes to present to the society a knowledgeable, skillfull,sensitive and ethically correct.    

scholarly journals ALTERNATING AND SYMMETRIC GROUPS WITH EULERIAN GENERATING GRAPH

2017 ◽  
Vol 5 ◽  
Author(s):  
ANDREA LUCCHINI ◽  
CLAUDE MARION
Keyword(s):  
Finite Group ◽  
Symmetric Group ◽  
Prime Number ◽  
Symmetric Groups ◽  
Alternating Group ◽  
Generating Graph ◽  
Alternating And Symmetric Groups ◽  
A Finite Group

Given a finite group $G$, the generating graph $\unicode[STIX]{x1D6E4}(G)$ of $G$ has as vertices the (nontrivial) elements of $G$ and two vertices are adjacent if and only if they are distinct and generate $G$ as group elements. In this paper we investigate properties about the degrees of the vertices of $\unicode[STIX]{x1D6E4}(G)$ when $G$ is an alternating group or a symmetric group of degree $n$. In particular, we determine the vertices of $\unicode[STIX]{x1D6E4}(G)$ having even degree and show that $\unicode[STIX]{x1D6E4}(G)$ is Eulerian if and only if $n\geqslant 3$ and $n$ and $n-1$ are not equal to a prime number congruent to 3 modulo 4.

Natural constructions of the Mathieu groups

1989 ◽  
Vol 106 (3) ◽  
pp. 423-429 ◽  
Author(s):  
R. T. Curtis
Keyword(s):  
Symmetric Groups ◽  
The Other ◽  
Simple Groups ◽  
Alternating Group ◽  
Transitive Permutation Group ◽  
French Mathematician ◽  
Exceptional Groups ◽  
Transitive Groups ◽  
Mathieu Groups ◽  
Alternating And Symmetric Groups

In the second half of the last century the French mathematician Emil Mathieu discovered two quintuply transitive permutation groups, now labelled M12 and M24, acting on twelve and twenty-four letters respectively. With the classification of finite simple groups complete we now know that any other quintuply transitive permutation group, on any number of letters, must contain the corresponding alternating group. Indeed, the only quadruply transitive groups, other than the alternating and symmetric groups, are the point stabilizers in M12 and M24, which are denoted by M11 and M23 respectively. To put it another way, the study of multiply (≥ 4-fold) transitive groups now means the study of the symmetric groups and the Mathieu groups. Apart from their beauty and interest in their own right the Mathieu groups are involved in many of the other sporadic simple groups: see ([2], p. 238). Thus a detailed understanding of the other exceptional groups necessitates an intimate knowledge of M12 and M24.

Language, Subjectivity, Culture, Comprehensiveness, and Structure

2017 ◽  
pp. 374-388
Author(s):  
Gerard Saucier
Keyword(s):  
Two Dimensions ◽  
The Other ◽  
Underlying Structure ◽  
Trait Variation ◽  
Personality Dimension ◽  
Different Types ◽  
Optimal Classification ◽  
Subjective States

We know that (besides dispositions) situations affect behavior. To understand the situational contributions to prediction, we need frameworks for cataloging the different types of situations. To this end, useful situation-classifications have emerged recently. This chapter considers several puzzles in arriving at an optimal classification of situations. Can we learn something from how language is used? Should subjective states count as a kind of situation? Is culture a situation? What else should we consider in endeavoring to make the situation-classification comprehensive? At the other extreme of parsimony, to what minimal underlying structure can situations be reduced? How might the respective structures of situations and personality be related? It is concluded that each personality dimension may have particularly diagnostic situations integral to the relevant trait variation. And there are empirical indications for two situation-dimensions apparently closely allied with two dimensions in affect and motivation.

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