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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

New criterions of existence and conjugacy of Hall subgroups of finite groups


Authors: Wenbin Guo and Alexander N. Skiba
Journal: Proc. Amer. Math. Soc. 139 (2011), 2327-2336
MSC (2010): Primary 20D10, 20D20
Published electronically: December 2, 2010
MathSciNet review: 2784797
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Abstract: In the paper, new criterions for existence and conjugacy of Hall subgroups of finite groups are given. In particular, the Schur-Zassenhaus theorem, Hall theorem and Čunihin theorem are generalized.


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Additional Information

Wenbin Guo
Affiliation: Department of Mathematics, University of Science and Technology of China, Hefei 230026, People’s Republic of China
Email: wbguo@ustc.edu.cn

Alexander N. Skiba
Affiliation: Department of Mathematics, Francisk Skorina Gomel State University, Gomel 246019, Belarus
Email: alexander.skiba49@gmail.com

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10675-5
PII: S 0002-9939(2010)10675-5
Keywords: Sylow subgroup, Hall subgroup, $\pi$-separable group, permutable subgroups, $C_{\pi}$-group.
Received by editor(s): February 23, 2010
Received by editor(s) in revised form: May 12, 2010, and June 19, 2010
Published electronically: December 2, 2010
Additional Notes: The research of the first author was supported by an NNSF grant of China
Communicated by: Jonathan I. Hall
Article copyright: © Copyright 2010 American Mathematical Society