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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

 

Formations of finite $ C_\pi$-groups


Authors: E. P. Vdovin, D. O. Revin and L. A. Shemetkov
Translated by: E. P. Vdovin
Original publication: Algebra i Analiz, tom 24 (2012), nomer 1.
Journal: St. Petersburg Math. J. 24 (2013), 29-37
MSC (2010): Primary 20F17
Published electronically: November 15, 2012
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Abstract: It is proved that the class of all finite $ C_\pi $-groups is closed under subdirect products. Conditions for a given formation of $ C_\pi $-groups to be saturated or partially saturated are found.


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Additional Information

E. P. Vdovin
Affiliation: Sobolev Institute of mathematics, pr. Academica Koptyuga 4, Novosibirsk 630090, Russia
Email: vdovin@math.nsc.ru

D. O. Revin
Affiliation: Sobolev Institute of mathematics, pr. Academica Koptyuga 4, Novosibirsk 630090, Russia
Email: revin@math.nsc.ru

L. A. Shemetkov
Affiliation: Francisk Skorina Gomel State University, ul. Sovetskaya 104, Gomel 246019, Belarus
Email: shemetkov@gsu.by

DOI: http://dx.doi.org/10.1090/S1061-0022-2012-01230-6
PII: S 1061-0022(2012)01230-6
Keywords: Formation, saturated formation, solubly saturated formation, $p$-solubly saturated formation, $\pi$-Hall subgroup, property $C_\pi$
Received by editor(s): October 6, 2010
Published electronically: November 15, 2012
Additional Notes: The first two authors were partially supported by RFBR (projects nos. 10-01-00391 and 10-01-90007) and by the Federal Target Program “Scientific and educational personnel of innovation Russia” for 2009–2013 (government contract no. 14.740.11.0346). The first author was also supported by the Deligne 2004 Balzan Prize in Mathematics. The third author was supported by BRFFR (grant no. $Φ$10P-231) and by the Ministry of Education of Belarus (grant no. 2008470).
Article copyright: © Copyright 2012 American Mathematical Society