Displaying similar documents to “On central nilpotency in finite loops with nilpotent inner mapping groups”

On the structure of finite loop capable nilpotent groups

Miikka Rytty (2010)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we consider finite loops and discuss the problem which nilpotent groups are isomorphic to the inner mapping group of a loop. We recall some earlier results and by using connected transversals we transform the problem into a group theoretical one. We will get some new answers as we show that a nilpotent group having either C p k × C p l , k > l ≥ 0 as the Sylow p -subgroup for some odd prime p or the group of quaternions as the Sylow 2 -subgroup may not be loop capable.

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 centrally nilpotent loops

L. V. Safonova, K. K. Shchukin (2000)

Commentationes Mathematicae Universitatis Carolinae

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Using a lemma on subnormal subgroups, the problem of nilpotency of multiplication groups and inner permutation groups of centrally nilpotent loops is discussed.

A note on loops of square-free order

Emma Leppälä, Markku Niemenmaa (2013)

Commentationes Mathematicae Universitatis Carolinae

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Let Q be a loop such that | Q | is square-free and the inner mapping group I ( Q ) is nilpotent. We show that Q is centrally nilpotent of class at most two.