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A Note on Products of Normal Subgroups

Published online by Cambridge University Press:  20 November 2018

T.S. Shores
T.S. Shores*
Affiliation:
University of Nebraska, Lincoln, Nebraska
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By a group theoretic class we mean a class of groups which contains the trivial group, denoted E, and any group isomorphic to a group in the class. Let I be a group theoretic class. Following P. Hall [4, p. 533], we define EI, CI, SI, QI, and NoI to be the (group theoretic) classes consisting of extensions of I groups by I groups, cartesian products of I groups, subgroups of I groups, homorphic images of I groups and products of two normal I subgroups of a group, respectively. If T is one of the above operations on classes of groups and TI = I, we say X is T closed.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 1 , February 1969 , pp. 21 - 24
Copyright
Copyright © Canadian Mathematical Society 1969

References

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