Almost cyclic groups

2005/11/16 by Bruce M. Ikenaga, Ikenaga, Bruce
Mathematics · #20E #20F #Advanced Operator Algebra Research #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.math/0511400

openalex publication_date 2005/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A group G is almost cyclic if there is an element x in G, such that for all g in G, there is an element y in G and an integer n with ygy^-1 = xⁿ (that is, every element is conjugate to some power of x). W. Ziller asked whether there are finitely-presented almost cyclic groups which are not cyclic in connection with work on closed geodesics. V. Guba constructed an infinite (non-cyclic) finitely generated almost cyclic group. The principal results of this paper are: Solvable almost cyclic groups are cyclic, and one-relator almost cyclic groups are cyclic.

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