Irreducible Automorphisms of Certainp-Groups

1977 ◽  
Vol 29 (2) ◽  
pp. 333-348 ◽  
Author(s):  
D. Ž. Djoković ◽  
J. Malzan
Keyword(s):  
Finite Field ◽  
Maximal Subgroup ◽  
Finite Groups ◽  
General Problem ◽  
The Other ◽  
Frattini Subgroup ◽  
Other Hand

The chief purpose of this paper is to find all pairs (G, θ) whereGis a finite specialp-group, andθis an automorphism ofGacting trivially on the Frattini subgroup and irreducibly on the Frattini quotient. This problem arises in the context of describing finite groups having an abelian maximal subgroup. In fact, we solve a more general problem for a wider class ofp-groups, which we callspecial F-groups,whereFis a finite field of characteristicp.We point out that ifpis odd, then anF-group has exponentp.On the other hand, every special 2-group is also a specialGF(2)-group.

Stall Control

1960 ◽  
Author(s):  
S. Drabek
Keyword(s):  
Gas Turbine ◽  
General Problem ◽  
The Other ◽  
Jet Engine ◽  
Other Hand ◽  
Stall Control

Compressor stall has had an increasing effect through the years upon gas turbine controls. The general problem was reasonably well known in the first decade of jet engine history after the “Whittle Engine”. The scheduling approach to the control of compressor stall established during this time has become rooted throughout the industry. On the other hand, an idealized approach based on sensing incipient stall remains an intriguing challenge.

scholarly journals Some bounds for the degree of commutativity of a p-group of maximal class

1995 ◽  
Vol 51 (3) ◽  
pp. 353-367
Author(s):  
Antonio Vera-López ◽  
Gustavo A. Fernández-Alcober
Keyword(s):  
Maximal Subgroup ◽  
Lower Bounds ◽  
Nilpotency Class ◽  
The Other ◽  
Maximal Class ◽  
Derived Length ◽  
Other Hand

In this paper we obtain several lower bounds for the degree of commutativity of a p-group of maximal class of order pm. All the bounds known up to now involve the prime p and are almost useless for small m. We introduce a new invariant b which is related with the commutator structure of the group G and get a bound depending only on b and m, not on p. As a consequence, we bound the derived length of G and the nilpotency class of a certain maximal subgroup in terms of b. On the other hand, we also generalise some results of Blackburn. Examples are given in order to check the sharpness of the bounds.

Local systems and Sylow subgroups in locally finite groups. II

1974 ◽  
Vol 75 (1) ◽  
pp. 1-22 ◽  
Author(s):  
A. Rae
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Local System ◽  
The Other ◽  
Locally Finite Group ◽  
Local Systems ◽  
Locally Finite ◽  
Sylow Subgroups ◽  
Locally Finite Groups ◽  
Other Hand

1.1. Introduction. In this paper, we continue with the theme of (1): the relationships holding between the Sπ (i.e. maximal π) subgroups of a locally finite group and the various local systems of that group. In (1), we were mainly concerned with ‘good’ Sπ subgroups – those which reduce into some local system (and are said to be good with respect to that system). Here, on the other hand, we are concerned with a very much more special sort of Sπ subgroup.

scholarly journals Explicit isogenies in quadratic time in any characteristic

2016 ◽  
Vol 19 (A) ◽  
pp. 267-282 ◽  
Author(s):  
Luca De Feo ◽  
Cyril Hugounenq ◽  
Jérôme Plût ◽  
Éric Schost
Keyword(s):  
Finite Field ◽  
Elliptic Curves ◽  
Large Class ◽  
The Other ◽  
Base Field ◽  
Other Hand ◽  
Previous Algorithm ◽  
The Cost ◽  
Interesting Alternative ◽  
Refined Version

Consider two ordinary elliptic curves$E,E^{\prime }$defined over a finite field$\mathbb{F}_{q}$, and suppose that there exists an isogeny$\unicode[STIX]{x1D713}$between$E$and$E^{\prime }$. We propose an algorithm that determines$\unicode[STIX]{x1D713}$from the knowledge of$E$,$E^{\prime }$and of its degree$r$, by using the structure of the$\ell$-torsion of the curves (where $\ell$ is a prime different from the characteristic $p$of the base field). Our approach is inspired by a previous algorithm due to Couveignes, which involved computations using the$p$-torsion on the curves. The most refined version of that algorithm, due to De Feo, has a complexity of $\tilde{O} (r^{2})p^{O(1)}$base field operations. On the other hand, the cost of our algorithm is$\tilde{O} (r^{2})\log (q)^{O(1)}$, for a large class of inputs; this makes it an interesting alternative for the medium- and large-characteristic cases.

A Distinção Gráfico-Linguístico e a Notação Musical

2018 ◽  
Vol 74 (4) ◽  
pp. 1465-1492
Author(s):  
Fabrício Pires Fortes
Keyword(s):  
General Problem ◽  
Graphical Representation ◽  
Visual Representations ◽  
The Other ◽  
Linguistic Representation ◽  
Musical Notation ◽  
Other Hand ◽  
Linguistic Representations ◽  
The One ◽  
Pictorial Representations

This paper examines the traditional musical notation from the viewpoint of the general problem concerning the types of visual representations. More specifically, we analyze this system in relation to the distinction between graphical and linguistic representations. We start by comparing this notation with the representational systems which are most commonly associated with such categories: on the one hand, pictorial representations as an example of a graphical representation; on the other hand, verbal writing usually associated with a linguistic representation. Then, we examine the traditional musical notation in relation to different ways of drawing the distinction graphic–linguistic, and we evaluate the applicability of such criteria to the former system. Finally, we present some general remarks about the legitimacy of this distinction both with respect to representational systems in general and to the specific case of the traditional musical notation.

On the Commutativity of Certain Division Rings

1953 ◽  
Vol 5 ◽  
pp. 242-244 ◽  
Author(s):  
Tadasi Nakayama
Keyword(s):  
Finite Field ◽  
Natural Number ◽  
Division Algebra ◽  
Division Ring ◽  
The Other ◽  
Division Rings ◽  
Other Hand

Formerly Hua [1] proved that if A is a division ring with centre Z and if there exists a natural number n such that an ∈ Z for every a ∈ A, then A is commutative; this generalizes Wedderburn's theorem on finite division rings. Another generalization of Wedderburn's theorem, due to Jacobson [3], asserts that every algebraic division algebra over a finite field is commutative. On the other hand, a theorem of Noether and Jacboson [3] states that every noncommutative algebraic division algebra contains an element which is not contained in the centre Z and is separable over Z.

scholarly journals Bounds for nilpotent-by-finite groups in certain varieties

2002 ◽  
Vol 73 (3) ◽  
pp. 393-404 ◽  
Author(s):  
G. Endimioni
Keyword(s):  
Finite Groups ◽  
Nilpotent Groups ◽  
The Other ◽  
Polycyclic Group ◽  
Burnside Problem ◽  
Metabelian Groups ◽  
Variety Of Groups ◽  
Other Hand ◽  
Locally Nilpotent Groups ◽  
Restricted Burnside Problem

AbstractLet and denote respectively the variety of groups of exponent dividing e, the variety of nilpotent groups of class at most c, the class of nilpotent groups and the class of finite groups. It follows from a result due to Kargapolov and Čurkin and independently to Groves that in a variety not containing all metabelian groups, each polycyclic group G belongs to . We show that G is in fact in , where c is an integer depending only on the variety. On the other hand, it is not always possible to find an integer e (depending only on the variety) such that G belongs to but we characterize the varieties in which that is possible. In this case, there exists a function f such that, if G is d-generated, then G ∈ So, when e = 1, we obtain an extension of Zel'manov's result about the restricted Burnside problem (as one might expect, this result is used in our proof). Finally, we show that the class of locally nilpotent groups of a variety forms a variety if and only if for some integers c′, e′.

scholarly journals Words of Engel type are concise in residually finite groups

2019 ◽  
Vol 09 (02) ◽  
pp. 1950012 ◽  
Author(s):  
Eloisa Detomi ◽  
Marta Morigi ◽  
Pavel Shumyatsky
Keyword(s):  
Finite Groups ◽  
The Other ◽  
Residually Finite ◽  
Verbal Subgroup ◽  
Other Hand ◽  
Residually Finite Groups ◽  
The One ◽  
Engel Word

Given a group-word [Formula: see text] and a group [Formula: see text], the verbal subgroup [Formula: see text] is the one generated by all [Formula: see text]-values in [Formula: see text]. The word [Formula: see text] is said to be concise if [Formula: see text] is finite whenever the set of [Formula: see text]-values in [Formula: see text] is finite. In 1960s, Hall asked whether every word is concise but later Ivanov answered this question in the negative. On the other hand, Hall’s question remains wide open in the class of residually finite groups. In the present paper we show that various generalizations of the Engel word are concise in residually finite groups.

Facing the Bounds of Tradition: Kant's Controversy with the Philosophisches Magazin

1998 ◽  
Vol 11 (2) ◽  
pp. 205-228 ◽  
Author(s):  
Yaron Senderowicz
Keyword(s):  
General Problem ◽  
Natural Science ◽  
A Priori ◽  
The Other ◽  
Main Subject ◽  
Traditional Concept ◽  
Other Hand ◽  
Synthetic A Priori ◽  
To Come ◽  
New Generation

The ArgumentThe main subject examined in this paper is Immanuel Kant's controversy with Philosophisches Magazin regarding Kant's new theory of judgments. J. A. Eberhard, editor of Philosophisches Magazin, and his colleagues wanted to vindicate the Wollfian traditional concept of judgments by undermining Kant's claims. As will be demonstrated, their arguments were effective mainly in exposing the ambiguity that was inherent in Kant's concept of the synthetic a priori; an ambiguity that resulted from Kant's desire—central to his critique of metaphysics—to present judgments pertaining to mathematics, (dogmatic) metaphysics, and pure natural science as judgments which shared a common form. Exposing this ambiguity was not the intended result, and it was insufficient for the purpose of vindicating the Wollfian tradition. The contributors to Philosophisches Magazin ignored the important properties shared by the class of judgments falling under Kant's concept of synthetic a priori judgments. They also ignored the fact that their position was unable to account for the logical phenomena that motivated Kant to present a new theory of judgments. On the other hand, Kant's theory of judgments was insensitive to the important differences that exist among the distinct types of judgments falling under his concept of a synthetic a priori judgment. This latter point is clearly shown in the controversy regarding the novelty of Kant's concept of a synthetic a priori judgment, and in the controversy regarding the function of intuitions within synthetic judgments.A result of the controversy was that Kant's concept of the synthetic a priori, which he believed to be an exact concept, was revealed to be a metaphor: no more than an invitation to view certain intellectual fields in the light of others. On the other hand, Eberhard and his colleagues failed to come up with satisfactory answers to Kant's questions within their traditional concept of judgment. Both parties refused to acknowledge this result. Consequently, the search for a new logic, a new architectonic order, and a new unity within reason became a general problem for the new generation of philosophers.

scholarly journals Growth sequences of finite groups V

1981 ◽  
Vol 31 (3) ◽  
pp. 374-375 ◽  
Author(s):  
D. Meier ◽  
James Wiegold
Keyword(s):  
Finite Group ◽  
Automorphism Group ◽  
Finite Groups ◽  
The Other ◽  
Direct Power ◽  
Easy Proof ◽  
Number Of Generators ◽  
Other Hand ◽  
Minimum Number

AbstractA short and easy proof that the minimum number of generators of the nth direct power of a non-trival finite group of order s having automorphism group of order a is more than logsn + logsa, n > 1. On the other hand, for non-abelian simple G and large n, d(Gn) is within 1 + e of logsn + logsa.

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