# commutative group

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## commutative group

[¦käm·yə‚tād·iv ‚grüp]
(mathematics)
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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Then (M, +) is a commutative group. Quick calculations reveal that M is an X-module under the operation xm = x [conjunction] m shown in (26) (see ):
The space A[P.sub.[phi]](R, C) constitutes a nonlinear space, endowed only with addition as a commutative group and a topology of a metric (and complete) space.
In this section A and B are commutative groups. For A we use multiplicative notation while for B we use the additive notation.
We prove that A and G/[C.sub.G] (A) are commutative groups. Now, G'' = 1 thus G' is commutative and A [less than or equal to] G' yields that A is commutative, as well.
of Oxford) construct an analogue of Makanin-Razborov diagrams and use it to give a description of the solution set of systems of equations over partially commutative groups. In order to describe the solutions of constrained generalized equations over a free monoid, the monograph develops a branching rewriting process for constrained generalized equations and defines the automorphism groups of coordinate groups for the parameterization of the solution sets.
If ([G.sub.1]; [x.sub.1]) and ([G.sub.2]; [x.sub.2]) are commutative groups, then [??] is a field.

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