Products of Subgroups Which Are Subgroups |
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| Authors: | Gil Kaplan Dan Levy |
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| Affiliation: | 1. School of Computer Sciences, The Academic College of Tel-Aviv-Yaffo , Tel-Aviv, Israel gilk@mta.ac.il;3. School of Computer Sciences, The Academic College of Tel-Aviv-Yaffo , Tel-Aviv, Israel |
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| Abstract: | We prove conditions for a product of distinct subgroups of an arbitrary group G to be a subgroup of G. In particular, the normal closure of any A ≤ G is equal to the product of some distinct conjugates of A. As an application of the later result we derive constraints on the size of a nontrivial conjugacy class of a finite non-Abelian simple group. |
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| Keywords: | 20D40 |
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