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Central product of groups

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A group-theoretical construction. A group is called a central product of two of its subgroups and if it is generated by them, if for any two elements and and if the intersection lies in its centre . In particular, for the central product turns out to be the direct product . If , and are arbitrary groups such that and if is a monomorphism, then the central product of and can be defined without assuming in advance that and are subgroups of a certain group .

References

[1] D. Gorenstein, "Finite groups" , Harper & Row (1968)
How to Cite This Entry:
Central product of groups. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Central_product_of_groups&oldid=40165
This article was adapted from an original article by N.N. Vil'yams (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article