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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.
Received January 1, 2017, published March 21, 2018
Citation:
S. V. Skresanov, “On new examples of hypocritical groups”, Sib. Èlektron. Mat. Izv., 15 (2018), 305–313
Linking options:
https://www.mathnet.ru/eng/semr918 https://www.mathnet.ru/eng/semr/v15/p305
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Abstract page: | 222 | Full-text PDF : | 46 | References: | 39 |
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