Subgroup

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Related to Proper subgroup: Simple group

subgroup

[′səb‚grüp]
(mathematics)
A subset N of a group G which is itself a group relative to the same operation.

Subgroup

 

in mathematics, a subset of elements of a group that itself forms a group with respect to the group operation. This means that a subgroup that contains the elements a and b will always contain a-1 and ab as well.

References in periodicals archive ?
1) The hypotheses are inherited by all proper subgroups, thus G is a group which is not p-nilpotent but whose proper subgroups are all p-nilpotent.
Thus K, K [intersection] N satisfy the hypotheses of the theorem in any case, so K is p-nilpotent, therefore G is a group which is not p-nilpotent but whose proper subgroups are all p-nilpotent.
p'] since that G is a group which is not nilpotent but whose proper subgroups are all nilpotent.

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