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== A subgroup <math>S</math> of a (typically abelian) group <math>G</math> 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== * {{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:Subgroup properties Category:Abelian group theory
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