A direct factor theorem for commutative group algebras

William Ullery

Commentationes Mathematicae Universitatis Carolinae (1992)

  • Volume: 33, Issue: 3, page 383-387
  • ISSN: 0010-2628

Abstract

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Suppose F is a field of characteristic p ≠ 0 and H is a p -primary abelian A -group. It is shown that H is a direct factor of the group of units of the group algebra F H .

How to cite

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Ullery, William. "A direct factor theorem for commutative group algebras." Commentationes Mathematicae Universitatis Carolinae 33.3 (1992): 383-387. <http://eudml.org/doc/247412>.

@article{Ullery1992,
abstract = {Suppose $F$ is a field of characteristic $p\ne 0$ and $H$ is a $p$-primary abelian $A$-group. It is shown that $H$ is a direct factor of the group of units of the group algebra $F H$.},
author = {Ullery, William},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {units of group algebras; $A$-groups; totally projective -group; group ring; -primary -group; direct factor},
language = {eng},
number = {3},
pages = {383-387},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A direct factor theorem for commutative group algebras},
url = {http://eudml.org/doc/247412},
volume = {33},
year = {1992},
}

TY - JOUR
AU - Ullery, William
TI - A direct factor theorem for commutative group algebras
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1992
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 33
IS - 3
SP - 383
EP - 387
AB - Suppose $F$ is a field of characteristic $p\ne 0$ and $H$ is a $p$-primary abelian $A$-group. It is shown that $H$ is a direct factor of the group of units of the group algebra $F H$.
LA - eng
KW - units of group algebras; $A$-groups; totally projective -group; group ring; -primary -group; direct factor
UR - http://eudml.org/doc/247412
ER -

References

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  1. Fuchs L., Infinite Abelian Groups, Volumes I and II, Academic Press, New York, 1970 and 1973. Zbl0338.20063
  2. Hill P., The classification of N -groups, Houston J. Math. 10 (1984), 43-55. (1984) Zbl0545.20042MR0736574
  3. Hill P., On the structure of abelian p -groups, Trans. Amer. Math. Soc. 288 (1985), 505-525. (1985) Zbl0573.20053MR0776390
  4. Hill P., Ullery W., A note on a theorem of May concerning commutative group algebras, Proc. Amer. Math. Soc. 110 (1990), 59-63. (1990) Zbl0704.20007MR1039530
  5. May W., Modular group algebras of totally projective p -primary groups, Proc. Amer. Math. Soc. 76 (1979), 31-34. (1979) Zbl0388.20041MR0534384
  6. May W., Modular group algebras of simply presented abelian groups, Proc. Amer. Math. Soc. 104 (1988), 403-409. (1988) Zbl0691.20008MR0962805
  7. Mollov T.Zh., Ulm invariants of Sylow p -subgroups of group algebras of abelian groups over fields of characteristic p , Pliska 2 (1981), 77-82. (1981) MR0633857
  8. Ullery W., An isomorphism theorem for commutative modular group algebras, Proc. Amer. Math. Soc. 110 (1990), 287-292. (1990) Zbl0712.20036MR1031452
  9. Warfield R., A classification theorem for abelian p -groups, Trans. Amer. Math. Soc. 210 (1975), 149-168. (1975) Zbl0324.20058MR0372071

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