Center of a Group

The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Center of a Group

 

(or central of a group), in mathematics. The center of a group is the set of all elements of the group that commute with every element of the group. In other words, it is the set of elements z such that zg = gz for every element g of the given group G. The center is a subgroup of G. It is transformed into itself under all automorphisms of G (seeISOMORPHISM). The center of the group of nonsingular matrices of order n is the subgroup of scalar matrices, that is, matrices of the form λE, where λ is a number and E is the identity matrix.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.