On Equality of Certain Automorphism Groups
Surjeet Kour, Vishakha

TL;DR
This paper investigates the structure and isomorphisms of automorphism groups in certain non-abelian groups, providing conditions for their equality and exploring automorphism group properties in finite p-groups.
Contribution
It establishes isomorphisms between automorphism groups of specific group decompositions and characterizes automorphism group equalities in finite non-abelian p-groups.
Findings
Existence of isomorphisms between automorphism groups of decomposed groups.
Necessary and sufficient conditions for automorphism group equality in p-groups.
Analysis of automorphism group identities in finite non-abelian p-groups.
Abstract
Let be a group, where is a purely non-abelian subgroup of and is a non-trivial abelian factor of . Then, for , we show that there exists an isomorphism such that . Also, for a finite non-abelian -group satisfying a certain natural hypothesis, we give some necessary and sufficient conditions for . Furthermore, for a finite non-abelian -group we study the equality of with .
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Taxonomy
TopicsFinite Group Theory Research · graph theory and CDMA systems · Limits and Structures in Graph Theory
