Essential subgroup

Updated on Dec 17, 2023

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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 S of a (typically abelian) group G 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

Essential subgroup Wikipedia

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