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proper subgroup (Definition)

A proper subgroup of a group $ G$ is a subgroup $ H$ of $ G$ such that $ H\ne G$.

The only subgroup of $ G$ that is not a proper subgroup is $ G$ itself, which may therefore occasionally be called an improper subgroup.



"proper subgroup" is owned by yark. [ full author list (2) | owner history (1) ]
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See Also: subgroup, group

Also defines:  improper subgroup
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Cross-references: subgroup, group
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This is version 4 of proper subgroup, born on 2002-06-27, modified 2006-10-28.
Object id is 3141, canonical name is ProperSubgroup.
Accessed 5706 times total.

Classification:
AMS MSC: 20A99 (Group theory and generalizations :: Foundations :: Miscellaneous)
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