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- W2512948929 abstract "Let G be a finite group and {sigma} = {{sigma}_i, i in I} be a partition of the set of all primes mathbb{P}. A set mathcal{H} of subgroups of G with 1 in mathcal{H} is said to be a complete Hall {sigma}-set of G if every non-identity member of mathcal{H} is a Hall {sigma}_i-subgroup of G. A subgroup H of G is said to be {sigma}-permutable if G possesses a complete Hall {sigma}-set mathcal{H} such that HA^x = A^xH for all A in mathcal{H} and all x in G. We say that a subgroup H of G is weakly {sigma}-permutable in G if there exists a {sigma}-subnormal subgroup T of G such that G = HT and H cap T leq H_{sigma}G. where H_{sigma}G is the subgroup of H generated by all those subgroups of H which are {sigma}-permutable in G. By using this new notion, we establish some new criterias for a group G to be a {sigma}-soluble and supersoluble, and also we give the conditions under which a normal subgroup of G is hypercyclically embedded." @default.
- W2512948929 created "2016-09-16" @default.
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- W2512948929 date "2016-08-10" @default.
- W2512948929 modified "2023-09-23" @default.
- W2512948929 title "On weakly $sigma$-permutable subgroups of finite groups" @default.
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- W2512948929 doi "https://doi.org/10.48550/arxiv.1608.03224" @default.
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