Nilpotent groups with three conjugacy classes of non-normal subgroups
author
Abstract:
Let $G$ be a finite group and $nu(G)$ denote the number of conjugacy classes of non-normal subgroups of $G$. In this paper, all nilpotent groups $G$ with $nu(G)=3$ are classified.
similar resources
nilpotent groups with three conjugacy classes of non-normal subgroups
let $g$ be a finite group and $nu(g)$ denote the number of conjugacy classes of non-normal subgroups of $g$. in this paper, all nilpotent groups $g$ with $nu(g)=3$ are classified.
full textnon-nilpotent groups with three conjugacy classes of non-normal subgroups
for a finite group $g$ let $nu(g)$ denote the number of conjugacy classes of non-normal subgroups of $g$. the aim of this paper is to classify all the non-nilpotent groups with $nu(g)=3$.
full textNilpotent conjugacy classes in the classical groups
The original title for this essay was ‘What you always wanted to know about nilpotence but were afraid to ask’. I have changed it, because that title is not likely to be an accurate description of the current version. It is my attempt to understand and explain nilpotent conjugacy classes in the classical complex semi-simple Lie algebras (and therefore also, through the exponential map, of the u...
full textTwisted Conjugacy Classes in Nilpotent Groups
A group is said to have the R∞ property if every automorphism has an infinite number of twisted conjugacy classes. We study the question whether G has the R∞ property when G is a finitely generated torsion-free nilpotent group. As a consequence, we show that for every positive integer n ≥ 5, there is a compact nilmanifold of dimension n on which every homeomorphism is isotopic to a fixed point ...
full textFINITE GROUPS WITH FIVE NON-CENTRAL CONJUGACY CLASSES
Let G be a finite group and Z(G) be the center of G. For a subset A of G, we define kG(A), the number of conjugacy classes of G that intersect A non-trivially. In this paper, we verify the structure of all finite groups G which satisfy the property kG(G-Z(G))=5, and classify them.
full textConjugacy in Normal Subgroups of Hyperbolic Groups
Let N be a finitely generated normal subgroup of a Gromov hyperbolic group G. We establish criteria for N to have solvable conjugacy problem and be conjugacy separable in terms of the corresponding properties of G/N . We show that the hyperbolic group from F. Haglund’s and D. Wise’s version of Rips’s construction is hereditarily conjugacy separable. We then use this construction to produce firs...
full textMy Resources
Journal title
volume 40 issue 5
pages 1291- 1300
publication date 2014-10-01
By following a journal you will be notified via email when a new issue of this journal is published.
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023