on weakly ss-quasinormal and hypercyclically embedded properties of finite groups
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abstract
a subgroup $h$ is said to be $s$-permutable in a group $g$, if $hp=ph$ holds for every sylow subgroup $p$ of $g$. if there exists a subgroup $b$ of $g$ such that $hb=g$ and $h$ permutes with every sylow subgroup of $b$, then $h$ is said to be $ss$-quasinormal in $g$. in this paper, we say that $h$ is a weakly $ss$-quasinormal subgroup of $g$, if there is a normal subgroup $t$ of $g$ such that $ht$ is $s$-permutable and $hcap t$ is $ss$-quasinormal in $g$. by assuming that some subgroups of $g$ with prime power order have the weakly $ss$-quasinormal properties, we get some new characterizations about the hypercyclically embedded subgroups of $g$. a series of known results in the literature are unified and generalized.
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On Weakly Ss-quasinormal and Hypercyclically Embedded Properties of Finite Groups
A subgroup H is said to be s-permutable in a group G, if HP = PH holds for every Sylow subgroup P of G. If there exists a subgroup B of G such that HB = G and H permutes with every Sylow subgroup of B, then H is said to be SS-quasinormal in G. In this paper, we say that H is a weakly SS-quasinormal subgroup of G, if there is a normal subgroup T of G such that HT is s-permutable and H ∩ T is SS-...
full texton weakly $ss$-quasinormal and hypercyclically embedded properties of finite groups
a subgroup $h$ is said to be $s$-permutable in a group $g$, if $hp=ph$ holds for every sylow subgroup $p$ of $g$. if there exists a subgroup $b$ of $g$ such that $hb=g$ and $h$ permutes with every sylow subgroup of $b$, then $h$ is said to be $ss$-quasinormal in $g$. in this paper, we say that $h$ is a weakly $ss$-quasinormal subgroup of $g$, if there is a normal subgroup ...
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full textOn Ss-quasinormal and Weakly S-permutable Subgroups of Finite Groups
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full textfinite groups with some ss-embedded subgroups
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Journal title:
international journal of group theoryPublisher: university of isfahan
ISSN 2251-7650
volume 3
issue 4 2014
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