Circularity of Finite Groups without Fixed Points |
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Authors: | Kostia I Beidar Wen-Fong Ke Hubert Kiechle |
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Institution: | (1) National Cheng Kung University, Tainan, Taiwan;(2) Universität Hamburg, Germany |
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Abstract: | 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, a 0 c, are such that (a)+b![ne](/content/u1j18778765vp3t5/xxlarge8800.gif) (c)+d. |
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Keywords: | 2000 Mathematics Subject Classifications: 20D60 51E05 |
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