On Nearly σ-Embedded Subgroups of Finite Groups
Let G be a finite group, σ={σi|i∈I} be some partition of the set of all primes and σ(G)={σi|σi∩π(G)≠∅}. We say that a subgroup H of G is nearly σ-embedded in G if there exists a σ-permutable subgroup T of G such that HT is a σ-permutable subgroup of G and H∩T≤HσeG, where HσeG is the subgroup of H generated by all those subgroups of H which are σ-permutably embedded in G. In this paper, we study the structure of G under the condition that some given subgroups of G are nearly σ-embedded in G. Some known results are generalized.
2018 ◽
Vol 11
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pp. 160
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2001 ◽
Vol 71
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pp. 169-176
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2013 ◽
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pp. 1350060
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1969 ◽
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pp. 359-362
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