Circularity of Finite Groups without Fixed Points

• Autores: Kostia I. Beidar, Wen-Fong Ke, Hubert Kiechle
• Localización: Monatshefte für mathematik, ISSN 0026-9255, Vol. 144, Nº 4, 2005, págs. 265-273
• Idioma: inglés
• DOI: 10.1007/s00605-004-0268-x
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• Resumen

  • Let be a fixed point free group given by the presentation where and are relative prime numbers, t = /s and s = gcd( ¿ 1,), and is the order of modulo . We prove that if (1) = 2, and (2) is embeddable into the multiplicative group of some skew field, then is circular. This means that there is some additive group N on which acts fixed point freely, and |((a)+b)((c)+d)| 2 whenever a,b,c,d N, a0c, are such that (a)+b(c)+d.