Centraliser dimension and universal classes of groups.

zbMath1118.20030arXivmath/0502498MaRDI QIDQ2371248

Ilya V. Kazachkov, Andrew J. Duncan, Vladimir N. Remeslennikov

Publication date: 2 July 2007

Published in: Sibirskie Èlektronnye Matematicheskie Izvestiya (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0502498

zbMATH Keywords

commutativitymalnormal subgroupsclasses of groupsalgebraic geometry of partially commutative groupscommutative transitivityconjugacy-separable groupslattices of centralisers

Mathematics Subject Classification ID

Noncommutative algebraic geometry (14A22) Chains and lattices of subgroups, subnormal subgroups (20E15) Decidability of theories and sets of sentences (03B25) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Quasivarieties and varieties of groups (20E10)

Related Items (14)

Groups with bounded centralizer chains and the Borovik-Khukhro conjecture ⋮ Universal equivalence of generalized Baumslag-Solitar groups ⋮ Pseudofinite groups as fixed points in simple groups of finite Morley rank ⋮ Computation of the centralizer dimension of generalized Baumslag-Solitar groups ⋮ Quasivarieties generated by partially commutative groups. ⋮ On the centralizer dimension and lattice of generalized Baumslag-Solitar groups ⋮ Centralizer dimensions and universal theories for partially commutative metabelian groups ⋮ Partially commutative metabelian groups: centralizers and elementary equivalence. ⋮ A note on the conjugacy problem for finite Sylow subgroups of linear pseudofinite groups ⋮ Centralizer dimensions of partially commutative metabelian groups ⋮ The structure of locally finite groups of finite c-dimension ⋮ Universal theories and centralizer dimensions of groups ⋮ On systems of equations over free partially commutative groups ⋮ Group signature formulas constructed from graphs

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