Circularity of finite groups without fixed points

Kostia I. Beidar, Wen-Fong Ke, Hubert Kiechle

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2 Citations (Scopus)

Abstract

Let Φ be a fixed point free group given by the presentation « A, B\,\vert\, A^\mu=1,\, B^\nu=A^t,\, BAB-1=Aρ» where μ and ρ are relative prime numbers, t = μ/s and s = gcd(ρ - 1,μ), and ν is the order of ρ modulo μ. We prove that if (1) ν = 2, and (2) Φ is embeddable into the multiplicative group of some skew field, then Φ is circular. This means that there is some additive group N on which Φ acts fixed point freely, and |(Φ(a)+b)≠(Φ(c)+d)| ≤ 2 whenever a,b,c,d N, a ≠ 0 ≠ c, are such that Φ(a)+b ≠ Φ(c)+d.

Original languageEnglish
Pages (from-to)265-273
Number of pages9
JournalMonatshefte fur Mathematik
Volume144
Issue number4
DOIs
Publication statusPublished - 2005 Apr 1

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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