On p-Regular G-Conjugacy Classes and the p-Structure of Normal Subgroups |
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| Authors: | Xiuyun Guo Xianhe Zhao K. P. Shum |
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| Affiliation: | 1. Department of Mathematics , Shanghai University , Shanghai , China xyguo@shu.edu.cn;3. Department of Mathematics , Shanghai University , Shanghai , China;4. Department of Mathematics , The University of Hong Kong , Hong Kong , China |
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| Abstract: | Let N be a p-solvable normal subgroup of a group G such that N contains a noncentral Sylow r (≠ p)-subgroup R of G. It is proved that the p-complements of N are nilpotent if |x G |=1 or m for every p-regular element x of N whose order is divisible by at most two distinct primes. Our result, therefore, gives some information concerning the nilpotence of some kind of subgroups of a group G. |
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| Keywords: | Conjugacy class sizes Normal subgroups p-Regular elements |
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