Isomorphism Commutative Group Algebras Units Direct Sum of Cyclics Splitting Groups
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Mathematical Journal, Vol. 23, No 3-4, (1997), 211p-224p
Let K be a field of characteristic p > 0 and let G be a direct
sum of cyclic groups, such that its torsion part is a p-group. If there exists
a K-isomorphism KH ∼= KG for some group H, then it is shown that
H ∼= G.
Let G be a direct sum of cyclic groups, a divisible group or a simply
presented torsion abelian group. Then KH ∼= KG as K-algebras for all
fields K and some group H if and only if H ∼= G.
∗ The work was supported by the National Fund “Scientific researches” and by the Ministry
of Education and Science in Bulgaria under contract MM 70/91.