Isomorphism of Commutative Modular Group Algebras

Danchev, P.. "Isomorphism of Commutative Modular Group Algebras." Serdica Mathematical Journal 23.3-4 (1997): 211-224. <http://eudml.org/doc/11614>.

@article{Danchev1997,
abstract = {∗ 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.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.},
author = {Danchev, P.},
journal = {Serdica Mathematical Journal},
keywords = {Isomorphism; Commutative Group Algebras; Units; Direct Sum of Cyclics; Splitting Groups; commutative group algebras; isomorphism problem; direct sums of cyclic groups; simply presented torsion Abelian groups},
language = {eng},
number = {3-4},
pages = {211-224},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Isomorphism of Commutative Modular Group Algebras},
url = {http://eudml.org/doc/11614},
volume = {23},
year = {1997},
}

TY - JOUR
AU - Danchev, P.
TI - Isomorphism of Commutative Modular Group Algebras
JO - Serdica Mathematical Journal
PY - 1997
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 23
IS - 3-4
SP - 211
EP - 224
AB - ∗ 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.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.
LA - eng
KW - Isomorphism; Commutative Group Algebras; Units; Direct Sum of Cyclics; Splitting Groups; commutative group algebras; isomorphism problem; direct sums of cyclic groups; simply presented torsion Abelian groups
UR - http://eudml.org/doc/11614
ER -