TY - JOUR
T1 - Circularity of finite groups without fixed points
AU - Beidar, Kostia I.
AU - Ke, Wen Fong
AU - Kiechle, Hubert
PY - 2005/4
Y1 - 2005/4
N2 - 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.
AB - 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.
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U2 - 10.1007/s00605-004-0268-x
DO - 10.1007/s00605-004-0268-x
M3 - Article
AN - SCOPUS:17444408108
SN - 0026-9255
VL - 144
SP - 265
EP - 273
JO - Monatshefte fur Mathematik
JF - Monatshefte fur Mathematik
IS - 4
ER -