Nilpotency of a group.
On \(p\)-nilpotency of finite group with normally embedded maximal subgroups of some Sylow subgroups
... a group G for which every subgroup of M(P ) is S-embedded in G, where P is a Sylow p-subgroup of G and p ∈ π(G) such that (|G|, p − 1) = 1 follows from [5, Theorem ...
8
Nilpotency and related properties of group extensions
... the nilpotency class of nilpotent wreath products in general^ but these bounds are of widely different ...the nilpotency class of any group extension satisfying Baumslag's sufficient condition is ...
79
Irreducible representation of finite metacyclic group of nilpotency class two of order 16
... symmetry group of a physical system affects the solutions of equations describing that system can be ...symmetric group is a particular case of the representation theory of finite groups, for which a ...
18
The exact number of conjugacy classes for 2 - generator p - groups of nilpotency class 2
... The major contribution of this thesis will be the new theoretical results on the exact number of conjugacy classes for 2-generator p-groups of class 2 (p an odd prime). This thesis also contributes to a greater challenge ...
17
Some numerical results on two classes of finite groups
... Polkouei, Some numerical results on finite non-abelian 2- generator p-groups of nilpotency class two , Annals Math Iasi, preprinted.. Sarmin, On some problems in group theory of probabil[r] ...
10
Topological loops with solvable multiplication groups of dimension at most six are centrally nilpotent
... centrally nilpotency of class two prop- erty for connected topological proper loops L of dimension ≤ 3 which have an at most six-dimensional solvable indecomposable Lie group as their multiplication ...
14
Conjugacy classes and graphs of two-groups of nilpotency class two
... in group theory over the past ...nilpotent group, but yet not ...of nilpotency class two where p is an odd prime, while in this research, the exact number of conjugacy classes of 2-generator 2-groups ...
24
The influence of weakly \(s\)-permutably embedded subgroups on the \(p\)-nilpotency of finite groups
... finite group called weakly s-permutably embedded ...finite group G is said to be weakly s-permutably embedded in G if there are a subnormal subgroup T of G and an s-permutably embedded subgroup H se of G ...
8
Some applications of Two-Generator p-Groups of Nilpotency class two
... Recent work of Beuerle and Kappe in [3] focus the classification on infinite metacylic groups and some of their applications including the nonabelian tensor squares, exterior squares, the symmetric products and the ...
11
Generalized commutativity degrees of some finite groups and their related graphs
... a group, which focuses only for dihedral ...the group except the elements in the ...n-th nilpotency degree of two subgroups of a finite group which is a generalization of the non-commuting ...
28
The homological functors of some finite two-generator two-groups of nilpotency class two
... a group including J G , G , the exterior square, the Schur multiplier, G , the symmetric square and J G are closely related to the nonabelian tensor square of the ...a group G, denoted as G G , is generated ...
20
On unipotent radicals of pseudo-reductive groups
... { D m (H)} m ≥ 0 in the usual way, and D m (H)(¯ k) is the m th term in the lower central series for the abstract group H(¯ k). We say that H is nilpotent if there exists some integer m such that D m (H) = 1. The ...
20
Conjugacy and order classes of two-generator p-groups of nilpotency class two
... GAP [11] is a system for computational discrete algebra, with emphasis on computational group theory. GAP provides a programming language, a library of functions that implement algebraic algorithms written in the ...
16
Commutativity degrees and related invariants of some finite nilpotent groups
... of nilpotency class ...a group G can be computed by dividing the number of conjugacy classes by the order of the ...of nilpotency class two where p is an odd prime has been computed by Ahmad in ...
23
Capability and homological functors of infinite two - generator groups of nilpotency class two
... A group G is said to be capable if there exists a group K such that K/Z (K) is isomorphic to ...a group G with G/T (G) of rank bigger than ...
17
Lie Nilpotent Group Algebras: A Survey
... nilpotent group algebras whose Lie nilpotency indices are next lower, namely 2p and 3p − 1 for p ≥ ...classifying group algebras which are Lie nilpotent having Lie nilpotency indices 2p, 3p − ...
8
NILPOTENCY AND SOLUBILITY OF GROUPS RELATIVE TO AN AUTOMORPHISM
... groups, nilpotency and solvability of groups related to the automorphism α are ...all nilpotency classes and the set of all solvability classes for the group G with respect to different automorphisms ...
13
On Some Problems in Group Theory of Probabilistic Nature
... nonabelian group has been introduced for symmetric groups by Erdos and Turan in ...of nilpotency class 2 based on the classification that has been done by Kappe ...
7
On one-sided Lie nilpotent ideals of associative rings
... Corollary 1. Let R be an associative ring which can be decomposed into a sum R = A + B of its Lie nilpotent subrings A and B. If at least one of these subrings is an one-sided ideal of R then the ring R is Lie solvable. ...
6
A retrospective analysis focusing on a group of patients with dual diagnosis treated by both mental health and substance use services
... impact” group is the most represented among dual-diagnosis patients, the “high impact” group, even if smaller, requires more intensive and expensive treatment ...
10