Equations over groups, and groups with one defining relation

DOI10.1007/BF00971461zbMath0579.20020OpenAlexW2036980258MaRDI QIDQ1067002

Sergei D. Brodsky

Publication date: 1984

Published in: Siberian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00971461

zbMATH Keywords

group ringsfree groupsFreiheitssatzlocally indicable groupsone-relator productsequations over groupsfinitely generated subgroupnormal closurecyclically reduced wordSN-groupSI-groupsoluble subnormal systemsubnormal system with torsion-free abelian factorstorsion-free one-relator group

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Group rings of infinite groups and their modules (group-theoretic aspects) (20C07) Generators, relations, and presentations of groups (20F05) Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations (20E06) Local properties of groups (20E25)

Related Items

On Groups with Finitely Many Conradian Orderings ⋮ The universal torsion-free image of a group ⋮ The genus problem for one-relator products of locally indicable groups ⋮ Free division rings of fractions of crossed products of groups with Conradian left-orders ⋮ On the dynamics of (left) orderable groups. ⋮ Pseudo-Sylvester domains and skew Laurent polynomials over firs ⋮ Two-generator one-relator groups and marked polytopes ⋮ Coherence and one-relator products of locally indicable groups ⋮ One-relator products of torsion-free groups ⋮ Equations over solvable groups ⋮ Relative hyperbolicity and similar properties of one-generator one-relator relative presentations with powered unimodular relator. ⋮ Yet another Freiheitssatz: Mating finite groups with locally indicable ones ⋮ Borel structures on the space of left‐orderings ⋮ Non-orientable surface-plus-one-relation groups. ⋮ Generalizations of the Burns–Hale theorem ⋮ Directed diagrammatic reducibility ⋮ Conjugacy in lattice-ordered groups and right ordered groups ⋮ ON SOLVABILITY OF REGULAR EQUATIONS IN THE VARIETY OF METABELIAN GROUPS ⋮ Zero divisors and units with small supports in group algebras of torsion-free groups ⋮ A remarkable family of left-ordered groups: central extensions of Hecke groups ⋮ TOPOLOGICAL SOLVABILITY OF EQUATIONS OVER GROUPS ⋮ Magnus intersections in one-relator products. ⋮ A Magnus extension for locally indicable groups ⋮ \(L^2\)-Betti numbers of one-relator groups. ⋮ Locally Graded Quotients of Locally Graded Groups ⋮ The strong Atiyah and Lück approximation conjectures for one-relator groups ⋮ ON THE LOCAL-INDICABILITY COHEN–LYNDON THEOREM ⋮ The structure of one-relator relative presentations and their centres ⋮ ONE-RELATOR QUOTIENTS OF GRAPH PRODUCTS ⋮ Locally indicable groups of finite Mal'tsev rank.

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