Commutative group algebras of highly torsion-complete abelian p -groups

Peter Vassilev Danchev

Commentationes Mathematicae Universitatis Carolinae (2003)

  • Volume: 44, Issue: 4, page 587-592
  • ISSN: 0010-2628

Abstract

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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).

How to cite

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Danchev, Peter Vassilev. "Commutative group algebras of highly torsion-complete abelian $p$-groups." Commentationes Mathematicae Universitatis Carolinae 44.4 (2003): 587-592. <http://eudml.org/doc/249171>.

@article{Danchev2003,
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).},
author = {Danchev, Peter Vassilev},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {high subgroups; torsion-complete groups; group algebras; direct factors; high subgroups; torsion-complete groups; modular group algebras; direct factors; isomorphism problem; Abelian -groups; algebraically compact groups; semisimple group algebras},
language = {eng},
number = {4},
pages = {587-592},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Commutative group algebras of highly torsion-complete abelian $p$-groups},
url = {http://eudml.org/doc/249171},
volume = {44},
year = {2003},
}

TY - JOUR
AU - Danchev, Peter Vassilev
TI - Commutative group algebras of highly torsion-complete abelian $p$-groups
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2003
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 44
IS - 4
SP - 587
EP - 592
AB - 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).
LA - eng
KW - high subgroups; torsion-complete groups; group algebras; direct factors; high subgroups; torsion-complete groups; modular group algebras; direct factors; isomorphism problem; Abelian -groups; algebraically compact groups; semisimple group algebras
UR - http://eudml.org/doc/249171
ER -

References

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  10. Danchev P.V., Sylow p -subgroups of abelian group rings, Serdica Math. J. 29 (2003), 33-44. (2003) Zbl1035.16025MR1981103
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  12. Danchev P.V., Torsion completeness of Sylow p -groups in semi-simple group rings, Acta Math. Sinica (2003). (2003) 
  13. Danchev P.V., Commutative group algebras of p ø m e g a + n -projective abelian groups, submitted. Zbl1111.20007
  14. Danchev P.V., S ( R G ) / G p is a Σ -group, in press. 
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