scholarly journals A Note on Primitive Permutation Groups of Prime Power Degree

2015 ◽  
Vol 2015 ◽  
pp. 1-4
Author(s):  
Qian Cai ◽  
Hua Zhang
Keyword(s):  
Prime Power ◽  
Permutation Groups ◽  
Simple Type ◽  
Present Stage ◽  
Primitive Groups ◽  
Short Survey ◽  
Product Action ◽  
Action Type ◽  
Affine Type

Primitive permutation groups of prime power degree are known to be affine type, almost simple type, and product action type. At the present stage finding an explicit classification of primitive groups of affine type seems untractable, while the product action type can usually be reduced to almost simple type. In this paper, we present a short survey of the development of primitive groups of prime power degree, together with a brief description on such groups.

scholarly journals A note on extremely primitive affine groups

2020 ◽  
Author(s):  
Timothy C. Burness ◽  
Adam R. Thomas
Keyword(s):  
Maximal Subgroups ◽  
Simple Groups ◽  
Primitive Permutation Group ◽  
Primitive Groups ◽  
Almost Simple Groups ◽  
Affine Groups ◽  
Point Stabilizer ◽  
Affine Type ◽  
Finite Primitive Permutation Group

Abstract Let G be a finite primitive permutation group on a set $$\Omega $$ Ω with non-trivial point stabilizer $$G_{\alpha }$$ G α . We say that G is extremely primitive if $$G_{\alpha }$$ G α acts primitively on each of its orbits in $$\Omega {\setminus } \{\alpha \}$$ Ω \ { α } . In earlier work, Mann, Praeger, and Seress have proved that every extremely primitive group is either almost simple or of affine type and they have classified the affine groups up to the possibility of at most finitely many exceptions. More recently, the almost simple extremely primitive groups have been completely determined. If one assumes Wall’s conjecture on the number of maximal subgroups of almost simple groups, then the results of Mann et al. show that it just remains to eliminate an explicit list of affine groups in order to complete the classification of the extremely primitive groups. Mann et al. have conjectured that none of these affine candidates are extremely primitive and our main result confirms this conjecture.

scholarly journals Coprime subdegrees of twisted wreath permutation groups

2019 ◽  
Vol 62 (4) ◽  
pp. 1137-1162
Author(s):  
Alexander Y. Chua ◽  
Michael Giudici ◽  
Luke Morgan
Keyword(s):  
Simple Group ◽  
Permutation Group ◽  
Permutation Groups ◽  
Primitive Permutation Group ◽  
Primitive Groups ◽  
Group A ◽  
Full Classification

AbstractDolfi, Guralnick, Praeger and Spiga asked whether there exist infinitely many primitive groups of twisted wreath type with non-trivial coprime subdegrees. Here, we settle this question in the affirmative. We construct infinite families of primitive twisted wreath permutation groups with non-trivial coprime subdegrees. In particular, we define a primitive twisted wreath group G(m, q) constructed from the non-abelian simple group PSL(2, q) and a primitive permutation group of diagonal type with socle PSL(2, q)m, and determine many subdegrees for this group. A consequence is that we determine all values of m and q for which G(m, q) has non-trivial coprime subdegrees. In the case where m = 2 and $q\notin \{7,11,29\}$, we obtain a full classification of all pairs of non-trivial coprime subdegrees.

NEW CONSTRUCTIONS OF SELF-COMPLEMENTARY CAYLEY GRAPHS

2021 ◽  
pp. 1-14
Author(s):  
CAI HENG LI ◽  
GUANG RAO ◽  
SHU JIAO SONG
Keyword(s):  
Cayley Graphs ◽  
Permutation Groups ◽  
Product Action ◽  
Generic Construction ◽  
Action Type ◽  
Vertex Primitive

Abstract Vertex-primitive self-complementary graphs were proved to be affine or in product action by Guralnick et al. [‘On orbital partitions and exceptionality of primitive permutation groups’, Trans. Amer. Math. Soc.356 (2004), 4857–4872]. The product action type is known in some sense. In this paper, we provide a generic construction for the affine case and several families of new self-complementary Cayley graphs are constructed.

The primitive permutation groups of degree less than 1000

1988 ◽  
Vol 103 (2) ◽  
pp. 213-238 ◽  
Author(s):  
John D. Dixon ◽  
Brian Mortimer
Keyword(s):  
Finite Groups ◽  
Primitive Group ◽  
Simple Groups ◽  
Permutation Groups ◽  
Finite Simple Groups ◽  
Primitive Groups ◽  
Concrete Form

Our object is to describe all of the-primitive permutation groups of degree less than 1000 together with some of their significant properties. We think that such a list is of interest in illustrating in concrete form the kinds of primitive groups which arise, in suggesting conjectures about primitive groups, and in settling small exceptional cases which often occur in proofs of theorems about permutation groups. The range that we consider is large enough to allow examples of most of the types of primitive group to appear. Earlier lists (of varying completeness and accuracy) of primitive groups of degree d have been published by: C. Jordan (1872) [21] ford≤ 17, by W. Burnside (1897) [5] ford≤ 8, by Manning (1929) [34–38] ford≤ 15, by C. C. Sims (1970) [45] ford≤ 20, and by B. A. Pogorelev (1980) [42] ford≤ 50. Unpublished lists have also been prepared by C. C. Sims ford≤ 50 and by Mizutani[41] ford≤ 48. Using the classification of finite simple groups which was completed in 1981 we have been able to extend the list much further. Our task has been greatly simplified by the detailed information about many finite simple groups which is available in theAtlas of Finite Groupswhich we will refer to as theAtlas[8].

scholarly journals Base sizes of primitive permutation groups

2021 ◽  
Author(s):  
Mariapia Moscatiello ◽  
Colva M. Roney-Dougal
Keyword(s):  
Permutation Group ◽  
Wreath Product ◽  
Permutation Groups ◽  
Minimal Size ◽  
Mathieu Group ◽  
Natural Action ◽  
Primitive Groups ◽  
Product Action ◽  
Pointwise Stabilizer

AbstractLet G be a permutation group, acting on a set $$\varOmega $$ Ω of size n. A subset $${\mathcal {B}}$$ B of $$\varOmega $$ Ω is a base for G if the pointwise stabilizer $$G_{({\mathcal {B}})}$$ G ( B ) is trivial. Let b(G) be the minimal size of a base for G. A subgroup G of $$\mathrm {Sym}(n)$$ Sym ( n ) is large base if there exist integers m and $$r \ge 1$$ r ≥ 1 such that $${{\,\mathrm{Alt}\,}}(m)^r \unlhd G \le {{\,\mathrm{Sym}\,}}(m)\wr {{\,\mathrm{Sym}\,}}(r)$$ Alt ( m ) r ⊴ G ≤ Sym ( m ) ≀ Sym ( r ) , where the action of $${{\,\mathrm{Sym}\,}}(m)$$ Sym ( m ) is on k-element subsets of $$\{1,\dots ,m\}$$ { 1 , ⋯ , m } and the wreath product acts with product action. In this paper we prove that if G is primitive and not large base, then either G is the Mathieu group $$\mathrm {M}_{24}$$ M 24 in its natural action on 24 points, or $$b(G)\le \lceil \log n\rceil +1$$ b ( G ) ≤ ⌈ log n ⌉ + 1 . Furthermore, we show that there are infinitely many primitive groups G that are not large base for which $$b(G) > \log n + 1$$ b ( G ) > log n + 1 , so our bound is optimal.

scholarly journals Affine Primitive Groups and Semisymmetric Graphs

10.37236/2549 ◽  
2013 ◽  
Vol 20 (2) ◽  
Author(s):  
Hua Han ◽  
Zaiping Lu
Keyword(s):  
Bipartite Graph ◽  
Complete Bipartite Graph ◽  
Infinite Family ◽  
Permutation Groups ◽  
Primitive Groups ◽  
The Third ◽  
Semisymmetric Graphs

In this paper, we investigate semisymmetric graphs which arise from affine primitive permutation groups. We give a characterization of such graphs, and then construct an infinite family of semisymmetric graphs which contains the Gray graph as the third smallest member. Then, as a consequence, we obtain a factorization,of the complete bipartite graph $K_{p^{sp^t},p^{sp^t}}$ into connected semisymmetric graphs, where $p$ is an prime, $1\le t\le s$ with $s\ge2$ while $p=2$.

scholarly journals Prolegomena to the Problem of Determination and Classification of Original Religious Beliefs

2007 ◽  
pp. 18-26
Author(s):  
Dmytro V. Bazyk
Keyword(s):  
Religious Beliefs ◽  
Scientific Research ◽  
Religious Studies ◽  
The Other ◽  
Aboriginal Peoples ◽  
Present Stage ◽  
History Of ◽  
Methodological Approaches ◽  
Theoretical Developments

At the present stage of scientific research, one of the undefined problems in religious studies is, first of all, the problem of the expediency and relevance of the use of the term "primitive religions" or "primitive religious beliefs" in relation to both representatives of Aboriginal peoples of the present and the analysis of the development of religions in the history of forms of religion. discovered in general. The problem of determining the original religion and its forms of expression is somewhat compounded by the fact that the use of special terminology in theoretical developments depends not only on the various features of research methodological approaches, but also on the language in which studies are commonly published. Therefore, the use of one or the other terminology requires the isolation of a possible synonym for relatively adequate nomination (naming) of these religious manifestations.

scholarly journals MINI-PARLIAMENTS IN THE POST-DICTATORSHIP DEMOCRACIES OF WESTERN EUROPE AND LATIN AMERICA

2020 ◽  
Vol 24 (4) ◽  
pp. 942-964
Author(s):  
Alexey S. Koshel
Keyword(s):  
Latin America ◽  
Russian Federation ◽  
Western Europe ◽  
Parliamentary Democracy ◽  
Present Stage ◽  
The Russian Federation ◽  
Ongoing Development ◽  
Parliamentary Procedure

The article investigtes the powers and parliamentary procedures in the standing committees and commissions of several countries of Western Europe and Latin America. The author believes that one of the modern paradigms for the development of parliamentary democracy is to strengthen the role of standing committees in the work of parliament by transferring to the committee level a number of constitutional powers of parliaments. In this regard, the author clarifies approaches to the classification of the committee structure of parliaments and looks at committee parliamentary procedures in Italy, Germany, Greece, Portugal, Spain, Brazil and Argentina at the present stage. The author comes to certain conclusions regarding the paradigm of the committee parliamentary procedure, including further improvement of domestic constitutional-legal matter in the context of the ongoing development of parliamentary democracy in the Russian Federation.

scholarly journals Canine Malignant Mammary Tumours II. Adenocarcinomas, Solid Carcinomas and Spindle Cell Carcinomas

1972 ◽  
Vol 9 (6) ◽  
pp. 447-470 ◽  
Author(s):  
W. Misdorp ◽  
E. Cotchin ◽  
J. F. Hampe ◽  
Anne G. Jabara ◽  
J. von Sandersleben
Keyword(s):  
Spindle Cell ◽  
Clinical Signs ◽  
Subjective Assessment ◽  
Simple Type ◽  
Well Differentiated ◽  
The Times ◽  
Lymphatic Permeation ◽  
Preliminary Classification ◽  
Mammary Adenocarcinomas

A preliminary classification of 130 canine mammary adenocarcinomas, 76 solid carcinomas, and nine spindle cell carcinomas, together with several subtypes, was constructed from pooled, selected (metastasized) material. Each tumour in this series was classified by subjective assessment of its quantitatively predominant histological picture. Many adenocarcinomas and solid carcinomas of simple type were infiltrative, and lymphatic permeation was often found. The complex types of adenocarcinomas and of solid carcinomas were expansive, and lymphatic permeation was rare. Some metastasized adenocarcinomas were well differentiated. The clinical signs, distribution of metastases and some preliminary data on the times of survival of dogs with various types of carcinomas are discussed.

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