Core of a subgroup
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)|
Core of a subgroup. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Core_of_a_subgroup&oldid=16708