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Title

Conjugacy growth series of groups

Author Valentin Mercier
Director of thesis Laura Ciobanu
Co-director of thesis none
Summary of thesis In this thesis we study the conjugacy growth series of several group constructions in terms of the standard and the conjugacy growth series of the building groups, with a specific generating set. This includes (1) groups of the form G L when L admits a Cayley graph that is a tree, (2) graph products, (3) a specific free product of Z ∗ Z with amalgamation over Z, and (4) some HNN-extensions of graph products over isomorphic subgraph products. For all the groups mentioned we prove that the radius of convergence of the conjugacy growth series is the same as the radius of convergence of the standard growth series. We give an explicit formula for the conjugacy growth series of the groups G Z, G (C 2 ∗ C 2 ), of the graph products, of a specific free product of Z ∗ Z with amalgamation over Z, of the HNN-extension of graph products over isomorphic subgraph products based on disjoint subgraphs, and for an HNN-extension of a group of the form H ∗ H over itself by swapping the factor groups. We also prove at the end that for two infinite cardinals κ 1 and κ 2 with κ 1 < κ 2 , there exists a group of cardinality κ 2 , with κ 1 for the cardinality of its set of conjugacy classes.
Status finished
Administrative delay for the defence 01.06.2017
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