On G-Covering Subgroup Systems for Some Saturated Formations of Finite Groups |
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| Authors: | Wenbin Guo Jianhong Huang Alexander N Skiba |
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| Institution: | 1. School of Mathematical Sciences , University of Science and Technology of China , Hefei , China wbguo@ustc.edu.cn;3. School of Mathematical Sciences , Jiangsu Normal University , Xuzhou , China;4. Department of Mathematics , Francisk Skorina Gomel State University , Gomel , Belarus |
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| Abstract: | Let ? be a class of groups and G a finite group. We call a set Σ of subgroups of G a G-covering subgroup system for ? if G ∈ ? whenever Σ ? ?. For a non-identity subgroup H of G, we put Σ H be some set of subgroups of G which contains at least one supplement in G of each maximal subgroup of H. Let p ≠ q be primes dividing |G|, P, and Q be non-identity a p-subgroup and a q-subgroup of G, respectively. We prove that Σ P and Σ P ∪ Σ Q are G-covering subgroup systems for many classes of finite groups. |
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| Keywords: | G-covering subgroup system Maximal subgroup p-group Supplement of subgroup Saturated formation |
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