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ISOLATED SUBGROUPS OF FINITE p-GROUPS

Part of: Representation theory of groups

Published online by Cambridge University Press:  01 October 2021

QIANGWEI SONG  and
LIJIAN AN Open the ORCID record for LIJIAN AN [Opens in a new window]
QIANGWEI SONG
Affiliation:
Mathematics Department, Shanxi Normal University, Linfen, Shanxi 041004, China e-mail: [email protected]
LIJIAN AN*
Affiliation:
Mathematics Department, Shanxi Normal University, Linfen, Shanxi 041004, China
*
e-mail: [email protected]
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Abstract

We say that a subgroup H is isolated in a group G if for each $x\in G$ either $x\in H$ or $\langle x\rangle \cap H={1}$ . We determine the structure of finite p-groups with isolated minimal nonabelian subgroups and finite p-groups with an isolated metacyclic subgroup.

Keywords

finite p-groupisolated subgroupmetacyclic subgroupHughes subgroup

MSC classification

Primary: 20D15: Nilpotent groups, $p$-groups
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 105 , Issue 3 , June 2022 , pp. 449 - 457
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Copyright
© 2021 Australian Mathematical Publishing Association Inc.

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Footnotes

This work was supported by NSFC (Nos. 11901367 and 11971280).

References

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