Some Remarks on Commuting Fixed Point Free Automorphisms of Groups

On fixed-point-free automorphisms

Article history: Received 10 June 2014 Available online xxxx Communicated by E.I. Khukhro

Fixed point free automorphisms of groups related to finite fields

Let G = Fqo 〈β〉 be the semidirect product of the additive group of the field of q = p elements and the cyclic group of order d generated by the invertible linear transformation β defined by multiplication by a power of a primitive root of Fq. We study endomorphisms of G. We find an arithmetic condition on d so that every endomorphism is determined by its values on (1, 1) and (0, β). When that i...

Automorphisms of Free Groups Have Finitely Generated Fixed Point Sets

An automorphism of a finitely generated free group F extends to a homeomorphism of the end completion E of F. The set of fixed points of this homeomorphism is finitely generated in a certain sense. In particular this implies that the subgroup of elements fixed by the automorphism is finitely generated in the usual sense. The emphasis on E instead of F in this paper is analogous to Thurston’s st...

Finite Groups with Fixed-point-free Automorphisms of Prime Order.

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Some Remarks on Symplectic Automorphisms

Some notes on ``Common fixed point of two $R$-weakly commuting mappings in $b$-metric spaces"

Very recently, Kuman et al. [P. Kumam, W. Sintunavarat, S. Sedghi, and N. Shobkolaei. Common Fixed Point of Two $R$-Weakly Commuting Mappings in $b$-Metric Spaces. Journal of Function Spaces, Volume 2015, Article ID 350840, 5 pages] obtained some interesting common fixed point results for two mappings satisfying generalized contractive condition in $b$-metric space without the assumption of the...