Since each finite

Abelian group and dihedral groups are determined by their endomorphism monoids in the class of all groups (Lemmas 2.

For a commutative ring R with identity 1 and a finite

abelian group G, written additively, let R[G] denote the group ring of G over R.

1 (Fundamental theorem of finite

abelian groups) Any finite

abelian group G can be written as a direct sum of cyclic groups in the following canonical way: G = [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], where every [k.

On the Neat Essential Extensions of

Abelian Group Journal of Business Strategies, 4 (1), 1-6.

From [2] and [5], (M, *) forms an

Abelian group with identity element [[mu].

Properties of A(n, H) and B(n, H) on additive

Abelian group G

Let G be an

Abelian group and let E be a Banach space.

The symmetries that underlie Shannon's sampling theorem and its more general multi-band version are used as a basis for an exposition of sampling theory in a locally compact

abelian group setting.

This is what is called a free

abelian group, where the second word derives from the name of the Norwegian mathematician Abel.

This note shows how to obtain an

abelian group with an addition like operation (Joyner 2002:70-72) beginning with a subtraction binary operation.

Q] has no normal

abelian group of finite index; therefore [G.

Then we exploit the fact that for a nondegenerate pairing on an

abelian group holds [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and hence [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and that any r [member of] S acts on v by the 1-dimensional character [[chi].

It is well known that all endomorphisms of an

Abelian group form a ring and many of their properties can be characterized by this ring.

Let be a graph with an arbitrary but fixed orientation, and let be an

Abelian group of order and with 0 as its identity element.

For any

abelian group P and any integer m > 0, we write [P.