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On ℱ-residuals of finite groups

Published online by Cambridge University Press:  17 April 2009

Wenbin Guo ,
K. P. Shum  and
A. N. Skiba
Wenbin Guo
Affiliation:
Department of Mathematics, Xuzhou Normal University, Xuzhou, 221009People's Republic of China e-mail: yzgwb@pub.yz.jsinfo.net
K. P. Shum
Affiliation:
Department of Mathematics, The Chinese University of Hong KongShatin, Hong KongPeople's Republic of China (SAR), e-mail: kpshum@math.cuhk.edu.hk
A. N. Skiba
Affiliation:
Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong, People's Republic of China (SAR) e-mail: kpshum@math.cuhk.edu.hk
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Abstract

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We prove that there exists a soluble, saturated and s-closed formation ℱ of groups such that the class (Gℱ | G is a group, Gℱ is the ℱ-residual of G) is not closed under subdirect products. This result a negative answer to an open problems recently proposed by L.A. Shemetkov in 1998.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 65 , Issue 2 , April 2002 , pp. 271 - 275
Copyright
Copyright © Australian Mathematical Society 2002

References

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