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Malnormal subgroups and Frobenius groups: basics and examples

Pierre de la Harpe, Claude Weber (2014)

Confluentes Mathematici

Malnormal subgroups occur in various contexts. We review a large number of examples, and compare the general situation to that of finite Frobenius groups of permutations.In a companion paper [18], we analyse when peripheral subgroups of knot groups and 3 -manifold groups are malnormal.

Maximal clones and maximal permutation groups

Péter P. Pálfy (2007)

Discussiones Mathematicae - General Algebra and Applications

A fundamental result in universal algebra is the theorem of Rosenberg describing the maximal subclones in the clone of all operations over a finite set. In group theory, the maximal subgroups of the symmetric groups are classified by the O'Nan-Scott Theorem. We shall explore the similarities and differences between these two analogous major results. In addition, we show that a primitive permutation group of diagonal type can be maximal in the symmetric group only if its socle is the direct product...

Multiples of left loops and vertex-transitive graphs

Eric Mwambene (2005)

Open Mathematics

Via representation of vertex-transitive graphs on groupoids, we show that left loops with units are factors of groups, i.e., left loops are transversals of left cosets on which it is possible to define a binary operation which allows left cancellation.

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