Core of a subgroup

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Let be a subgroup of . The core of is the maximal subgroup of that is normal in (cf. also Normal subgroup). It follows that

If the index , then divides .

Let and define the permutation representation of on the set of right cosets of in . Then its kernel is the core of in .


[a1] M. Suzuki, "Group theory" , I , Springer (1982)
[a2] W.R. Scott, "Group theory" , Dover, reprint (1987) (Original: Prentice-Hall, 1964)
How to Cite This Entry:
Core of a subgroup. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article