Surfaces and the Second Homology of a Group.
A finite group whose irreducible characters are rational valued is called a rational or a Q-group. In this paper we obtain various results concerning the structure of a Sylow 2-subgroup of a solvable Q-group.
2000 Mathematics Subject Classification: Primary 20C07, 20K10, 20K20, 20K21; Secondary 16U60, 16S34.Let PG be the abelian modular group ring of the abelian group G over the abelian ring P with 1 and prime char P = p. In the present article,the p-primary components Up(PG) and S(PG) of the groups of units U(PG) and V(PG) are classified for some major classes of abelian groups. Suppose K is a first kind field with respect to p in char K ≠ p and A is an abelian p-group. In the present work, the p-primary...