Finite equilibrated groups
Finite equilibrated groups
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DOI：
10.1017/s0305004100001560
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发表时间：
1996-11
影响因子：
0.8
通讯作者：
Norman Blackburn;Marian Deaconescu;Avinoam Mann
中科院分区：
文献类型：
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作者：
Norman Blackburn;Marian Deaconescu;Avinoam Mann
如果H，K是群G的子群，则HK是G的子群当且仅当HK=KH。如果H≤NG(K)或K≤NG(H)，则这个条件肯定成立。但大多数基团也可以表达为HK，在那里H和K都不正常。本文考虑没有子群G1的群G可以表示为G1的非正规子群的乘积。这样的群体被认为是平衡的。因此，当且仅当H、K和HK是G的子群时，G是平衡的当且仅当H≤NG(K)或K≤NG(H)。
If H, K are subgroups of a group G, then HK is a subgroup of G if and only if HK = KH. This condition certainly holds if H ≤ NG(K) or K ≤ NG(H). But the majority of groups can also be expressed as HK, where neither H nor K is normal. In this paper we consider groups G for which no subgroup G1 can be expressed as the product of non-normal subgroups of G1. Such a group is said to be equilibrated. Thus G is equilibrated if and only if either H ≤ NG(K) or K ≤ NG(H) whenever H, K and HK are subgroups of G.