Displaying similar documents to “Finite groups with an automorphism of prime order whose fixed points are in the Frattini of a nilpotent subgroup”

On complemented subgroups of finite groups

Long Miao (2006)

Czechoslovak Mathematical Journal

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A subgroup H of a group G is said to be complemented in G if there exists a subgroup K of G such that G = H K and H ∩ K = 1 . In this paper we determine the structure of finite groups with some complemented primary subgroups, and obtain some new results about p -nilpotent groups.

On central nilpotency in finite loops with nilpotent inner mapping groups

Markku Niemenmaa, Miikka Rytty (2008)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we consider finite loops whose inner mapping groups are nilpotent. We first consider the case where the inner mapping group I ( Q ) of a loop Q is the direct product of a dihedral group of order 8 and an abelian group. Our second result deals with the case where Q is a 2 -loop and I ( Q ) is a nilpotent group whose nonabelian Sylow subgroups satisfy a special condition. In both cases it turns out that Q is centrally nilpotent.

Some remarks on groups in which elements with the same p -power commute

Patrizia Longobardi, Mercede Maj (1999)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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In this paper we characterize certain classes of groups G in which, from x p = y p ( x , y ∈ G , p a fixed prime), it follows that x ⁢ y = y ⁢ x . Our results extend results previously obtained by other authors, in the finite case.