• Title/Summary/Keyword: self-normalizing subgroups

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ON MINIMAL NON-𝓠𝓝𝑺-GROUPS

  • Han, Zhangjia;Shi, Huaguo;Chen, Guiyun
    • Bulletin of the Korean Mathematical Society
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    • v.51 no.4
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    • pp.1063-1073
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    • 2014
  • A finite group G is called a $\mathcal{QNS}$-group if every minimal subgroup X of G is either quasinormal in G or self-normalizing. In this paper the authors classify the non-$\mathcal{QNS}$-groups whose proper subgroups are all $\mathcal{QNS}$-groups.

FINITE GROUPS WHICH ARE MINIMAL WITH RESPECT TO S-QUASINORMALITY AND SELF-NORMALITY

  • Han, Zhangjia;Shi, Huaguo;Zhou, Wei
    • Bulletin of the Korean Mathematical Society
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    • v.50 no.6
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    • pp.2079-2087
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    • 2013
  • An $\mathcal{SQNS}$-group G is a group in which every proper subgroup of G is either s-quasinormal or self-normalizing and a minimal non-$\mathcal{SQNS}$-group is a group which is not an $\mathcal{SQNS}$-group but all of whose proper subgroups are $\mathcal{SQNS}$-groups. In this note all the finite minimal non-$\mathcal{SQNS}$-groups are determined.