Core of a subgroup
From Encyclopedia of Mathematics
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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 .
References
[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: http://encyclopediaofmath.org/index.php?title=Core_of_a_subgroup&oldid=16708
Core of a subgroup. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Core_of_a_subgroup&oldid=16708
This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article