On abelian group actions with TNI-centralizers
G\"ulin Ercan, \.Ismail \c{S}. G\"ulo\u{g}lu

TL;DR
This paper investigates the structure of finite groups with abelian automorphism groups having TNI-centralizers, establishing bounds on the group's Fitting length based on properties of the centralizer and automorphism group.
Contribution
It introduces new bounds on the Fitting length of finite groups with abelian automorphism groups possessing TNI-centralizers, linking group structure to automorphism properties.
Findings
G is solvable with Fitting length at most h(C_G(A)) + ℓ(A)
If C_G(A) is nonnormal, then h(G) ≤ ℓ(A) + 3
Provides structural insights into groups with TNI-centralizers and abelian automorphisms
Abstract
A subgroup of a group is said to be a TNI-subgroup if for any Let be an abelian group acting coprimely on the finite group by automorphisms in such a way that \, for all is a solvable TNI-subgroup of . We prove that is a solvable group with Fitting length is at most . In particular whenever is nonnormal. Here, is the Fitting length of and is the number of primes dividing counted with multiplicities.
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Taxonomy
TopicsProtein Tyrosine Phosphatases · Finite Group Theory Research · Magnetism in coordination complexes
