Abstract:A new class of abelian $p$-groups with all high subgroups isomorphic is defined. Commutative modular and semisimple group algebras over such groups are examined. The results obtained continue our recent statements published in Comment. Math. Univ. Carolinae (2002).
Keywords: high subgroups, torsion-complete groups, group algebras, direct factors
AMS Subject Classification: 20C07, 16S34, 16U60, 20K