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ON CONDITIONALLY PERMUTABLE SUBGROUPS AND SUPERSOLUBILITY
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AI
DOI：10.21136/cmj.2026.0451-25.png)
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Abstract
En 中文
Let H, K be subgroups of G. Then H and K are called c-permutable in G if there exists an element x is an element of G such that HKx = (KH)-H-x. By imposing c-permutability conditions on the members of a maximal subgroup series of G, we give some new criteria for the supersolubility of a finite group. We prove that if G is a soluble group with a maximal subgroup series 1 = M-0 < M-1 < & mldr; < Ms-1 < M-s = G, where Mi is c-permutable in G for every i = 0, 1, & mldr;, s, then G is supersoluble. On this basis, if G is not soluble, but we have the condition that Mi is c-permutable in Mi+1 (0 <= i <= s - 1), then G is also supersoluble. These results provide new characterizations of supersoluble groups.
Keywords:
finite group
supersolublilty
c-permutable subgroup
maximal subgroup series
Journal
C
IF:
0.5
Papers:
60
Citations:
0