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  and , (M, *) forms an Abelian group
with identity element [[mu].
Properties of A(n, H) and B(n, H) on additive Abelian group
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
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.