Essential subgroup

In mathematics, specifically group theory, a subgroup $S$ of a (typically abelian) group $G$ is called an essential subgroup if whenever $H$ is a non-trivial subgroup of $G$ , the intersection of $S$ and $H$ is non-trivial; that is, $S \cap H \neq {e}$ , where $e$ is the group's identity. The concept has been generalized to essential submodules.

References

↑ Griffith (1970), p. 19.

Griffith, Phillip A. (1970). Infinite Abelian Group Theory. Chicago Lectures in Mathematics. University of Chicago Press. ISBN 0-226-30870-7.

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[FOOTNOTEGriffith197019-1] Griffith (1970), p. 19.