Finite $p$-groups whose normal closures of non-normal subgroups have two orders

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J. Korean Math. Soc. 2022; 59(4): 805-819

Online first article June 14, 2022 Printed July 1, 2022

Lifang Wang

Shanxi Normal University

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We describe the structure of finite $p$-groups in which all normal closures of non-normal subgroups have two orders for $p>2$.

Keywords: Finite $p$-groups, non-normal subgroups, normal closure

MSC numbers: Primary 20D10, 20D15

Supported by: This work was financially supported by NSFC (no. 11971280, 11771258).