Isomorphism of commutative group algebras of -mixed splitting groups over rings of characteristic zero

Peter Vassilev Danchev

Mathematica Bohemica (2006)

  • Volume: 131, Issue: 1, page 85-93
  • ISSN: 0862-7959

Abstract

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Suppose is a -mixed splitting abelian group and is a commutative unitary ring of zero characteristic such that the prime number satisfies . Then and are canonically isomorphic -group algebras for any group precisely when and are isomorphic groups. This statement strengthens results due to W. May published in J. Algebra (1976) and to W. Ullery published in Commun. Algebra (1986), Rocky Mt. J. Math. (1992) and Comment. Math. Univ. Carol. (1995).

How to cite

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Danchev, Peter Vassilev. "Isomorphism of commutative group algebras of $p$-mixed splitting groups over rings of characteristic zero." Mathematica Bohemica 131.1 (2006): 85-93. <http://eudml.org/doc/249902>.

@article{Danchev2006,
abstract = {Suppose $G$ is a $p$-mixed splitting abelian group and $R$ is a commutative unitary ring of zero characteristic such that the prime number $p$ satisfies $p\notin \mathop \{\text\{inv\}\}(R) \cup \mathop \{\text\{zd\}\}(R)$. Then $R(H)$ and $R(G)$ are canonically isomorphic $R$-group algebras for any group $H$ precisely when $H$ and $G$ are isomorphic groups. This statement strengthens results due to W. May published in J. Algebra (1976) and to W. Ullery published in Commun. Algebra (1986), Rocky Mt. J. Math. (1992) and Comment. Math. Univ. Carol. (1995).},
author = {Danchev, Peter Vassilev},
journal = {Mathematica Bohemica},
keywords = {group algebras; isomorphisms; $p$-mixed splitting groups; rings with zero characteristic; group algebras; isomorphism problem; -mixed splitting Abelian groups},
language = {eng},
number = {1},
pages = {85-93},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Isomorphism of commutative group algebras of $p$-mixed splitting groups over rings of characteristic zero},
url = {http://eudml.org/doc/249902},
volume = {131},
year = {2006},
}

TY - JOUR
AU - Danchev, Peter Vassilev
TI - Isomorphism of commutative group algebras of $p$-mixed splitting groups over rings of characteristic zero
JO - Mathematica Bohemica
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 131
IS - 1
SP - 85
EP - 93
AB - Suppose $G$ is a $p$-mixed splitting abelian group and $R$ is a commutative unitary ring of zero characteristic such that the prime number $p$ satisfies $p\notin \mathop {\text{inv}}(R) \cup \mathop {\text{zd}}(R)$. Then $R(H)$ and $R(G)$ are canonically isomorphic $R$-group algebras for any group $H$ precisely when $H$ and $G$ are isomorphic groups. This statement strengthens results due to W. May published in J. Algebra (1976) and to W. Ullery published in Commun. Algebra (1986), Rocky Mt. J. Math. (1992) and Comment. Math. Univ. Carol. (1995).
LA - eng
KW - group algebras; isomorphisms; $p$-mixed splitting groups; rings with zero characteristic; group algebras; isomorphism problem; -mixed splitting Abelian groups
UR - http://eudml.org/doc/249902
ER -

References

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