Since each finite

Abelian group is determined by its endomorphism semigroup in the class of all groups ([7], Theorem 4.

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

Abelian group G

The ternar, 1) whose ternary operation is composed of its two binary natural operations, 2) which is an

Abelian group with respect to the addition and a loop with respect to the multiplication, and 3) which has the properties (26) and (27), has been considered in [49], therefore it is called a Veblen-Wedderburn system (also said to be a quasifield).

Words obey the group laws a(bc) = ab(c), ai = ia = a, and aa' = a'a = i and the

abelian group law ab = ba.

Therefore

abelian groups are completely characterized as subtractive groupoids.

Sooryanarayana, Hamiltonian Distance Generating sets of an

Abelian Group, Proceedings, National Seminar on Recent developments in applications of Mathematics held at Sri Padmavathi Mahila University, Tirupati, Andhra Pradesh, India, during 21-22, March 2005.

It is known that every

Abelian group G has the zero-endomorphism corresponding to the maximal congruence G x G.

9, P is an elementary

abelian group and so P does not have an element of order 4, a contradiction.

alpha]] ([alpha] [member of] C) forms an

Abelian group with the Dirichlet series multiplication followed by a number of applications.

q] is an

Abelian group composed of reduced divisors on C.

Proposition 22 If FL(V,W) is nonempty, then FL(V,W) is an

abelian group.

Cholewa (2) demonstrated that Skof's theorem is also valid if the relevant domain is replaced by an

Abelian group.

d]; it is isomorphic to the free

Abelian group on d generators.

Schwartz worked on abstract algebra, determining when a finite

Abelian group can be partitioned into cosets of distinct subgroups.

For a category F of finitely generated left F-modules, the Grothendieck group G(F) is the

abelian group generated by symbols [M], one for every isomorphism class of modules M in F and relations [M] = [L] + [N] for any short exact sequence 0 [right arrow] L [right arrow] M [right arrow] N [right arrow] 0 in F.