Nearly m-embedded subgroups and solvability of finite groups |
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Authors: | Juping Tang |
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Institution: | Wuxi Institute of Technology, Wuxi, People’s Republic of China |
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Abstract: | A subgroup A of a finite group G is called {1≤G}-embedded in G if for each two subgroups K≤H of G, where K is a maximal subgroup of H, A either covers the pair (K,H) or avoids it. Moreover, a subgroup H of G is called nearly m-embedded in G if G has a subgroup T and a {1≤G}-embedded subgroup C such that G?=?HT and H∩T≤C≤H. In this paper, we mainly prove that G is solvable if and only if its Sylow 3-subgroups, Sylow 5-subgroups and Sylow 7-subgroups are nearly m-embedded in G. |
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Keywords: | Composition factor finite groups nearly m-embedded subgroup PSL(2 8) Sylow subgroups |
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