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Group Extensions with Infinite Conjugacy Classes

Jean-Philippe Préaux (2013)

Confluentes Mathematici

We characterize the group property of being with infinite conjugacy classes (or icc, i.e. infinite and of which all conjugacy classes except { 1 } are infinite) for groups which are extensions of groups. We prove a general result for extensions of groups, then deduce characterizations in semi-direct products, wreath products, finite extensions, among others examples we also deduce a characterization for amalgamated products and HNN extensions. The icc property is correlated to the Theory of von Neumann...

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