A solvable group admitting a regular splitting automorphism of prime order is nilpotent

1978 ◽  
Vol 17 (5) ◽  
pp. 402-406 ◽  
Author(s):  
E. I. Khukhro
Keyword(s):  
Solvable Group ◽  
Prime Order ◽  
Regular Splitting ◽  
Splitting Automorphism

On the Largest Irreducible Character Degree of a Finite Solvable Group

2010 ◽  
Vol 17 (spec01) ◽  
pp. 925-927 ◽  
Author(s):  
M. H. Jafari
Keyword(s):  
Finite Group ◽  
Wreath Product ◽  
Solvable Group ◽  
Irreducible Character ◽  
Prime Order ◽  
Character Degree ◽  
Finite Solvable Group ◽  
A Finite Group ◽  
Irreducible Character Degree

Let b(G) denote the largest irreducible character degree of a finite group G. In this paper, we prove that if G is a solvable group which does not involve a section isomorphic to the wreath product of two groups of equal prime order p, and if b(G) < pn, then |G:Op(G)|p < pn.

On a class of finite solvable groups

2013 ◽  
Vol 11 (9) ◽  
Author(s):  
James Beidleman ◽  
Hermann Heineken ◽  
Jack Schmidt
Keyword(s):  
Solvable Group ◽  
Prime Order ◽  
Solvable Groups ◽  
Finite Solvable Group ◽  
Normal Subgroups ◽  
Nilpotent Residual ◽  
Quotient Groups ◽  
Subnormal Subgroups

AbstractA finite solvable group G is called an X-group if the subnormal subgroups of G permute with all the system normalizers of G. It is our purpose here to determine some of the properties of X-groups. Subgroups and quotient groups of X-groups are X-groups. Let M and N be normal subgroups of a group G of relatively prime order. If G/M and G/N are X-groups, then G is also an X-group. Let the nilpotent residual L of G be abelian. Then G is an X-group if and only if G acts by conjugation on L as a group of power automorphisms.

Nilpotency of solvable groups admitting a splitting automorphism of prime order

1980 ◽  
Vol 19 (1) ◽  
pp. 77-84 ◽  
Author(s):  
E. I. Khukhro
Keyword(s):  
Prime Order ◽  
Solvable Groups ◽  
Splitting Automorphism

On groups with a splitting automorphism of prime order

1992 ◽  
Vol 34 (2) ◽  
pp. 360-362
Author(s):  
E. I. Khukhro
Keyword(s):  
Prime Order ◽  
Splitting Automorphism

A GENERALIZED FIXED-POINT-FREE ACTION

2012 ◽  
Vol 12 (03) ◽  
pp. 1250172
Author(s):  
İSMAİL Ş. GÜLOĞLU ◽  
GÜLİN ERCAN
Keyword(s):  
Fixed Point ◽  
Finite Group ◽  
Solvable Group ◽  
Upper Bound ◽  
Prime Order ◽  
Free Action ◽  
Group A ◽  
Point Free Action ◽  
A Finite Group ◽  
Coprime Order

In this paper we study the structure of a finite group G admitting a solvable group A of automorphisms of coprime order so that for any x ∈ CG(A) of prime order or of order 4, every conjugate of x in G is also contained in CG(A). Under this hypothesis it is proven that the subgroup [G, A] is solvable. Also an upper bound for the nilpotent height of [G, A] in terms of the number of primes dividing the order of A is obtained in the case where A is abelian.

scholarly journals Some Remarks on the Regular Splitting of Quasi-Polynomials with Two Delays. Characterization of Double Roots in Degenerate Cases

2020 ◽  
Vol 53 (2) ◽  
pp. 4386-4391
Author(s):  
Alejandro Martínez-González ◽  
César-Fernando Méndez-Barrios ◽  
Silviu-Iulian Niculescu
Keyword(s):  
Regular Splitting ◽  
Two Delays ◽  
Degenerate Cases

𝒫-characters and the structure of finite solvable groups

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Jiakuan Lu ◽  
Kaisun Wu ◽  
Wei Meng
Keyword(s):  
Finite Group ◽  
Maximal Subgroup ◽  
Solvable Group ◽  
Irreducible Character ◽  
Solvable Groups ◽  
Irreducible Constituent ◽  
A Finite Group

AbstractLet 𝐺 be a finite group. An irreducible character of 𝐺 is called a 𝒫-character if it is an irreducible constituent of (1_{H})^{G} for some maximal subgroup 𝐻 of 𝐺. In this paper, we obtain some conditions for a solvable group 𝐺 to be 𝑝-nilpotent or 𝑝-closed in terms of 𝒫-characters.

Functional encryption for computational hiding in prime order groups via pair encodings

2017 ◽  
Vol 86 (1) ◽  
pp. 97-120 ◽  
Author(s):  
Jongkil Kim ◽  
Willy Susilo ◽  
Fuchun Guo ◽  
Man Ho Au
Keyword(s):  
Prime Order ◽  
Functional Encryption

scholarly journals On the normalizers of elements of prime order in simple groups

1974 ◽  
Vol 29 (3) ◽  
pp. 387-400 ◽  
Author(s):  
J.A Cohn
Keyword(s):  
Prime Order ◽  
Simple Groups
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