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On the Schur multiplier of a quotient of a direct product of groups

Published online by Cambridge University Press:  17 April 2009

Graham Ellis
Graham Ellis
Affiliation:
Department of Mathematics, National University of Ireland, Galway, Ireland e-mail: graham.ellis@ucg.ie
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Abstract

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We use a nonabelian exterior product to strengthen two old and basic results on the Schur multiplier of a (central) quotient of a direct product of groups.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 58 , Issue 3 , December 1998 , pp. 495 - 499
Copyright
Copyright © Australian Mathematical Society 1998

References

[1]Brown, R., Johnson, D.L. and Robertson, E.F., ‘Some computations of nonabelian tensor products of groups’, J. Algebra 111 (1987), 177–202.CrossRefGoogle Scholar
[2]Brown, R. and Loday, J.-L., ‘Van Kampen theorems for diagrams of spaces’, Topology 26 (1987), 311–335.CrossRefGoogle Scholar
[3]Eckmann, B., Hilton, P.J. and Stammbach, U., ‘On the Schur multiplicator of a central quotient of a direct product of groups’, J. Pure Appl. Algebra 3 (1973), 73–82.CrossRefGoogle Scholar
[4]Ellis, G., ‘Nonabelian exterior products of groups and an exact sequence in the homology of groups’, Glasgow Math. J. 29 (1987), 13–19.CrossRefGoogle Scholar
[5]Ellis, G., ‘Capability, homology, and central series of a pair of groups’, J. Algebra 179 (1995), 31–46.CrossRefGoogle Scholar
[6]Ellis, G., ‘The Schur multiplier of a pair of groups’, Appl. Categ. Structures (to appear).Google Scholar
[7]Ellis, G., ‘On the capability of groups’, Proc. Edinburgh Math. Soc. (to appear).Google Scholar
[8]Ellis, G., ‘A bound for the derived and Frattini subgroups of a prime-power group’, Proc. Amer. Math. Soc. 126 (1998), 2513–2523.CrossRefGoogle Scholar
[9]Wiegold, J., ‘Some groups with nontrivial multiplicators’, Math. Z. 120 (1971), 307–308.CrossRefGoogle Scholar