Mathematical logic, algebra and number theory

On new examples of hypocritical groups

S. V. Skresanov

Novosibirsk State University, ul. Pirogova, 2, 630090, Novosibirsk, Russia

Abstract: A group $ G $ is called hypocritical if whenever $ G $ lies in a locally finite variety generated by a section closed class of groups $ \mathfrak{X} $, then $ G $ belongs to $ \mathfrak{X} $. We prove that some coprime extensions of a $ p $-group are hypocritical. The first example is given when such a $ p $-group is nonabelian.

Keywords: locally finite varieties, finite groups, extraspecial $ p $-groups.

UDC: 512.542, 512.544.5

MSC: 20D99, 20F50

Received January 1, 2017, published March 21, 2018

Language: English

DOI: 10.17377/semi.2018.15.027

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