A generalized fixed point free automorphism of prime power order

Date

2012-06-01

Author

Ercan, Gülin

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Let G be a finite group and alpha be an automorphism of G of order p(n) for an odd prime p. Suppose that alpha acts fixed point freely on every alpha-invariant p'-section of G, and acts trivially or exceptionally on every elementary abelian alpha-invariant p-section of G. It is proved that G is a solvable p-nilpotent group of nilpotent length at most n + 1, and this bound is best possible.

Subject Keywords

Noncoprime automorphism, Nilpotent length, P-length, Exceptional action

URI

https://hdl.handle.net/11511/43870

Journal

International Journal of Algebra and Computation

DOI

https://doi.org/10.1142/s0218196712500294

Collections

Department of Mathematics, Article

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A GENERALIZED FIXED-POINT-FREE ACTION Güloğlu, İsmail Şuayip; Ercan, Gülin (2013-05-01) In this paper we study the structure of a finite group G admitting a solvable group A of automorphisms of coprime order so that for any x epsilon C-G(A) of prime order or of order 4, every conjugate of x in G is also contained in C-G(A). Under this hypothesis it is proven that the subgroup [G, A] is solvable. Also an upper bound for the nilpotent height of [G, A] in terms of the number of primes dividing the order of A is obtained in the case where A is abelian.
On abelian group actions with TNI-centralizers Ercan, Gülin (2019-07-03) 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.
Finite groups having centralizer commutator product property Ercan, Gülin (2015-12-01) Let a be an automorphism of a finite group G and assume that G = {[g, alpha] : g is an element of G} . C-G(alpha). We prove that the order of the subgroup [G, alpha] is bounded above by n(log2(n+1)) where n is the index of C-G(alpha) in G.
A filtration on equivariant Borel-Moore homology Bingham, Aram; Can, Mahir Bilen; Ozan, Yıldıray (2019-07-04) Let G / H be a homogeneous variety and let X be a G-equivariant embedding of G / H such that the number of G-orbits in X is finite. We show that the equivariant Borel-Moore homology of X has a filtration with associated graded module the direct sum of the equivariant Borel-Moore homologies of the G-orbits. If T is a maximal torus of G such that each G-orbit has a T-fixed point, then the equivariant filtration descends to give a filtration on the ordinary Borel-Moore homology of X. We apply our findings to c...
On the influence of fixed point free nilpotent automorphism groups Ercan, Gülin (2017-12-01) A finite group FH is said to be Frobenius-like if it has a nontrivial nilpotent normal subgroup F with a nontrivial complement H such that for all nonidentity elements . Let FH be a Frobenius-like group with complement H of prime order such that is of prime order. Suppose that FH acts on a finite group G by automorphisms where in such a way that In the present paper we prove that the Fitting series of coincides with the intersections of with the Fitting series of G, and the nilpotent length of G exceeds the...

Citation Formats

G. Ercan, “A generalized fixed point free automorphism of prime power order,” International Journal of Algebra and Computation, pp. 0–0, 2012, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/43870.