Noncoprime action of a cyclic group

Date

2024-04-01

Author

Ercan, Gülin
Güloğlu, İsmail Ş.

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Let A be a finite nilpotent group acting fixed point freely on the finite (solvable) group G by automorphisms. It is conjectured that the nilpotent length of G is bounded above by ℓ(A), the number of primes dividing the order of A counted with multiplicities. In the present paper we consider the case A is cyclic and obtain that the nilpotent length of G is at most 2ℓ(A) if |G| is odd. More generally we prove that the nilpotent length of G is at most 2ℓ(A)+c(G;A) when G is of odd order and A normalizes a Sylow system of G where c(G;A) denotes the number of trivial A-modules appearing in an A-composition series of G.

Subject Keywords

Automorphism, Fixed point free action, Nilpotent length

URI

https://hdl.handle.net/11511/108180

Collections

Department of Mathematics, Article