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Algebra i logika, 2011, Volume 50, Number 3, Pages 326–350 (Mi al489)  
This article is cited in 6 scientific papers (total in 6 papers)

Finite Alperin 2-groups with cyclic second commutants

B. M. Veretennikov

Ural State Technical University, Ekaterinburg, Russia
Full-text PDF (219 kB) Citations (6)
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Abstract: An Alperin group is a group in which every 2-generated subgroup has a cyclic commutant. Previously, we constructed examples of finite Alperin 2-groups with second commutant isomorphic to $Z_2$ or $Z_4$. Here, it is proved that for any natural $n$, there exists a finite Alperin 2-group whose second commutant is isomorphic to $Z_{2^n}$.
Keywords: 2-group, Alperin group, commutant, representation of groups in terms of generators and defining relations.
Received: 24.03.2010
English version:
Algebra and Logic, 2011, Volume 50, Issue 3, Pages 226–244
DOI: https://doi.org/10.1007/s10469-011-9137-6
Bibliographic databases:
Document Type: Article
UDC: 512.54
Language: Russian
Citation: B. M. Veretennikov, “Finite Alperin 2-groups with cyclic second commutants”, Algebra Logika, 50:3 (2011), 326–350; Algebra and Logic, 50:3 (2011), 226–244
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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