Every finite

Abelian group is determined by its endomorphism monoid in the class of all groups.

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].

2 If G is an

abelian group of order n and n is divisible by m then there exists a subgroup of G with order m.

In fact the two objects are not truly equivalent, in that the information contained in matroids over Z is richer, because there are many finite

abelian groups with the same cardinality.

On the Neat Essential Extensions of

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

Throughout this brief article, let G be an

abelian group with p-component of torsion [G.

1] is compact), and so are united by working with locally compact

abelian groups.

This note shows how to obtain an

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

t]([chi])) are located in different direct summands of the

abelian group [B.

We end with a proof that, also in the case of monoids and

abelian groups, normal and central extensions coincide.

Any locally compact

abelian group M defines a sheaf yM of

abelian groups on Top; this (Yoneda) provides a fully faithful embedding of the (additive, but not abelian) category Tab of locally compact

abelian groups into the (abelian) category Tab of sheaves of

abelian groups on Top.

The second conjecture concerns the study of infinite almost

abelian groups, more precisely we ask whether the super tree property at a small cardinal kappa implies that every almost free

abelian group of size kappa is free.