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Evetts, Alex

Rational growth in virtually abelian groups. (English) Zbl 1515.20217

Ill. J. Math. 63, No. 4, 513-549 (2019).
Summary: We show that any subgroup of a finitely generated virtually abelian group \(G\) grows rationally relative to \(G\), that the set of right cosets of any subgroup of \(G\) grows rationally, and that the set of conjugacy classes of \(G\) grows rationally. These results hold regardless of the choice of finite weighted generating set for \(G\).

Cited in 5 Documents

MSC:

20F65 Geometric group theory
20E45 Conjugacy classes for groups
05E16 Combinatorial aspects of groups and algebras
20F05 Generators, relations, and presentations of groups
20F69 Asymptotic properties of groups
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\textit{A. Evetts}, Ill. J. Math. 63, No. 4, 513--549 (2019; Zbl 1515.20217)
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