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Malnormal subgroups and Frobenius groups: basics and examples. With an appendix by Denis Osin. (English) Zbl 1327.20030

From the text: 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 [P. de la Harpe and C. Weber, Confluentes Math. 6, No. 1, 41-64 (2014; Zbl 1319.57010)], we analyse when peripheral subgroups of knot groups and \(3\)-manifold groups are malnormal.
The main purpose of the present subsidiary paper is to collect in Section 3 several examples of pairs \[ \text{(infinite group, malnormal subgroup)} \] which are classical. Section 2 is a reminder of basic elementary facts on malnormal subgroups. In Section 4, we allude to some facts concerning the more general notion of almost malnormal subgroup, important in the theory of relatively hyperbolic groups. We conclude in Section 5 by comparing malnormal subgroups in infinite groups with finite Frobenius groups.

MSC:

20E07 Subgroup theorems; subgroup growth
20B07 General theory for infinite permutation groups
20B05 General theory for finite permutation groups
20F05 Generators, relations, and presentations of groups
57M25 Knots and links in the \(3\)-sphere (MSC2010)
57N10 Topology of general \(3\)-manifolds (MSC2010)

Citations:

Zbl 1319.57010
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References:

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