Essential subgroup
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. The concept was generalized to essential submodules.
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. The concept was generalized to essential submodules.
Definition
[edit]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
[edit]- Phillip A. Griffith (1970). Infinite Abelian group theory. Chicago Lectures in Mathematics. University of Chicago Press. p. 19. ISBN 0-226-30870-7.
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