Subgroup

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subgroup

[′səb‚grüp]
(mathematics)
A subset N of a group G which is itself a group relative to the same operation.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

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.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
References in periodicals archive ?
([1], III, 5.2) Suppose G is a group which is not p-nilpotent but whose proper subgroups are all p-nilpotent.
(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.
Clearly [J.sub.1] and [J.sub.1] are additive proper subgroups of J whose union is J.
Lemma 2.5.([13]) Suppose that G is a group which is not p--nilpotent but whose proper subgroups are all p--nilpotent.

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