完全条件可换与F-群

Completely Conditionally Permutable and F-groups

称群G的子群H在G中完全条件可换,如果对于G的每一个子群K,都存在x∈<H,K>,使得HKx=KxH.本文利用了子群的完全可换性得到了F-群的一个判别准则.

We call a subgroup H of G completely conditionally permutable in G if for every subgroup K of G there exists an element x ∈ 〈 H,K 〉 such that HK^x = K^xH. In this paper we obtain a criterion of .F-group by the completely conditionally permutable of subgroups.