Central factor

In mathematics, a central factor of a group G is a subgroup H such that there exists a subgroup K such that HK=G and every element of H commutes with every element of K. The subgroup K can in fact be taken to be the centralizer of H in G. The subgroup K is also a central factor. If H is a central factor, then every inner automorphism of G restricts to an inner automorphism of H. In particular, a central factor is always a normal subgroup. Every normal subgroup of a central factor of a group G is a normal subgroup of G.

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