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Difference between revisions of "Essential subgroup"

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(Start article: Essential subgroup)
 
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==References==
 
==References==
*  Phillip A. Griffith, ''Infinite Abelian group theory'', Chicago  Lectures in Mathematics (University of Chicago Press, 1970) ISBN 0-226-30870-7 p.19
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*  Phillip A. Griffith, ''Infinite Abelian group theory'', Chicago  Lectures in Mathematics (University of Chicago Press, 1970) {{ISBN|0-226-30870-7}} p.19

Latest revision as of 14:23, 12 November 2023

A subgroup that determines much of the structure of its containing group. The concept may be generalized to essential submodules.

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

  • Phillip A. Griffith, Infinite Abelian group theory, Chicago Lectures in Mathematics (University of Chicago Press, 1970) ISBN 0-226-30870-7 p.19
How to Cite This Entry:
Essential subgroup. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Essential_subgroup&oldid=54406