Essential subgroup: Difference between revisions
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In [[mathematics]], especially in the area of [[abstract algebra|algebra]] studying the theory of [[abelian group]]s, an '''essential subgroup''' is a subgroup that determines much of the structure of its containing group. | In [[mathematics]], especially in the area of [[abstract algebra|algebra]] studying the theory of [[abelian group]]s, an '''essential subgroup''' is a subgroup that determines much of the structure of its containing group. | ||
Revision as of 02:33, 2 February 2009
In mathematics, especially in the area of algebra studying the theory of abelian groups, an essential subgroup is a subgroup that determines much of the structure of its containing group.
Definition
A subgroup of a (typically abelian) group is said to be essential if whenever H is a non-trivial subgroup of G, the intersection of S and H is non-trivial: here "non-trivial" means "containing an element other than the identity".
References
- Phillip A. Griffith (1970). Infinite Abelian group theory. University of Chicago Press. ISBN 0-226-30870-7.