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Central subgroup

From Wikipedia, the free encyclopedia

In mathematics, in the field of group theory, a subgroup of a group is termed central if it lies inside the center of the group.

Given a group , the center of , denoted as , is defined as the set of those elements of the group which commute with every element of the group. The center is a characteristic subgroup. A subgroup of is termed central if .

Central subgroups have the following properties:

References

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  • "Centre of a group", Encyclopedia of Mathematics, EMS Press, 2001 [1994].