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The multiplicator of a regular product of groups

Published online by Cambridge University Press:  17 April 2009

William Haebich
Affiliation:
Department of Pure Mathematics, School of General Studies, Australian National University, Canberra, ACT.
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Abstract

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It is shown that if G is an arbitrary regular product of its subgroups Aλ, ∈ ϵ I, then the multiplicator, M(G), is the director product of the M(Aλ) together with a certain other group. This extends a calculation of M(A1 × A2) due to Schur. As an application, we find the multiplicator of a vertai wreath product A wrVB where A is abelian. A representing group for a finite regular product is also constructed.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Blackburn, Norman, “Some homology groups of wreathe productsIllinois J. Math. 16 (1972), 116129.CrossRefGoogle Scholar
[2]Golovin, O.N., “Nilpotent products of groupsAmer. Math. Soc. Transl. (2) 2 (1956), 89115.Google Scholar
[3]Hall, Marshall Jr, The theory of groups (The Macmillan Company, New York, 1959).Google Scholar
[4]Hall, P. and Hartley, B., “The stability group of a series of subgroupsProc. London Math. Soc. (3) 16 (1966), 139.CrossRefGoogle Scholar
[5]Moran, S., “Associative operations on groups. IProc. London Math. Soc. (3) 6 (1956), 381596.Google Scholar
[6]Moran, S., “Associative operations on groups. IIProc. London Math. Soc. (3) 8 (1958), 548568.CrossRefGoogle Scholar
[7]Schur, J., “Über die Darstellung der endlichen Gruppen durch gebrochene lineare SubstitutionenJ. reine angew. Math. 127 (1904), 2050.Google Scholar
[8]Schur, J., “Untersuchungen über die Darstellungen der endlichen Gruppen durch gebrochene lineare SubstitutionenJ. reine angew. Math. 132 (1907), 85137.Google Scholar
[9]Wiegold, James, “Nilpotent products of groups with amalgamationsPubl. Math. Debrecen 6 (1959), 131168.CrossRefGoogle Scholar
[10]Wiegold, James, “The multiplicator of a direct productQuart. J. Math. Oxford (2) 22 (1971), 103105.CrossRefGoogle Scholar