On abelian group actions with TNI-centralizers


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Ercan G., Guloglu I. S.

COMMUNICATIONS IN ALGEBRA, cilt.47, ss.3003-3006, 2019 (SCI-Expanded, Scopus) identifier identifier

Özet

A subgroup H of a group G is said to be a TNI-subgroup if for any Let A be an abelian group acting coprimely on the finite group G by automorphisms in such a way that for all is a solvable TNI-subgroup of G. We prove that G is a solvable group with Fitting length h(G) is at most . In particular whenever is nonnormal. Here, h(G) is the Fitting length of G and is the number of primes dividing A counted with multiplicities.