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. | ||
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==References== | ==References== | ||
* {{cite book | author=Phillip A. Griffith | title=Infinite Abelian group theory | series=Chicago Lectures in Mathematics | publisher=University of Chicago Press | year=1970 | isbn=0-226-30870-7 | page=19}} | * {{cite book | author=Phillip A. Griffith | title=Infinite Abelian group theory | series=Chicago Lectures in Mathematics | publisher=University of Chicago Press | year=1970 | isbn=0-226-30870-7 | page=19}}[[Category:Suggestion Bot Tag]] | ||
Latest revision as of 17:00, 13 August 2024
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.