Automorphisms of higher rank lamplighter groups

DOI10.1142/S0218196715500411zbMath1342.20037arXiv1412.2271OpenAlexW2963115852MaRDI QIDQ3467631

Peter N.-S. Wong, Melanie Stein, Jennifer Taback

Publication date: 4 February 2016

Published in: International Journal of Algebra and Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1412.2271

zbMATH Keywords

automorphism groupsCayley graphsouter automorphismstwisted conjugacy classesDiestel-Leader graphsDiestel-Leader groupslamplighter groupsReidemeister numbersproperty \(R_\infty\)

Mathematics Subject Classification ID

Conjugacy classes for groups (20E45) Generators, relations, and presentations of groups (20F05) Geometric group theory (20F65) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Automorphisms of infinite groups (20E36) Automorphism groups of groups (20F28) Fixed points and coincidences in algebraic topology (55M20) Groups acting on trees (20E08)

Related Items (7)

The \(\mathrm{R}_\infty\)-property for nilpotent quotients of Baumslag-Solitar groups ⋮ Higher rank lamplighter groups are graph automatic ⋮ Conjugacy languages in virtual graph products ⋮ The R∞ property for crystallographic groups of Sol14 ⋮ Reidemeister classes in some lamplighter-type groups ⋮ Extensions of automorphisms of self-similar groups ⋮ Reidemeister classes in lamplighter-type groups

Cites Work

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• A non-cyclic one-relator group all of whose finite quotients are cyclic
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