Central product of groups
From Encyclopedia of Mathematics
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=15113
Central product of groups. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Central_product_of_groups&oldid=15113
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