Partial augmentations power property: A Zassenhaus Conjecture related problem |
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Authors: | Leo Margolis Ángel del Río |
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Institution: | Departamento de Matemáticas, Universidad de Murcia, 30100 Murcia, Spain |
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Abstract: | Zassenhaus conjectured that any unit of finite order in the integral group ring of a finite group G is conjugate in the rational group algebra of G to an element in ±G. We review the known weaker versions of this conjecture and introduce a new condition, on the partial augmentations of the powers of a unit of finite order in , which is weaker than the Zassenhaus Conjecture but stronger than its other weaker versions.We prove that this condition is satisfied for units mapping to the identity modulo a nilpotent normal subgroup of G. Moreover, we show that if the condition holds then the HeLP Method adopts a more friendly form and use this to prove the Zassenhaus Conjecture for a special class of groups. |
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Keywords: | 16U60 16S34 20C05 20C10 Integral group ring Groups of units Zassenhaus Conjecture Partial augmentation |
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