Previous |  Up |  Next

Article

Keywords:
units of group algebras; $A$-groups
Summary:
Suppose $F$ is a field of characteristic $p\neq 0$ 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 $F H$.
References:
[F] Fuchs L.: Infinite Abelian Groups. Volumes I and II, Academic Press, New York, 1970 and 1973. Zbl 0338.20063
[H1] Hill P.: The classification of $N$-groups. Houston J. Math. 10 (1984), 43-55. MR 0736574 | Zbl 0545.20042
[H2] Hill P.: On the structure of abelian $p$-groups. Trans. Amer. Math. Soc. 288 (1985), 505-525. MR 0776390 | Zbl 0573.20053
[HU] Hill P., Ullery W.: A note on a theorem of May concerning commutative group algebras. Proc. Amer. Math. Soc. 110 (1990), 59-63. MR 1039530 | Zbl 0704.20007
[M1] May W.: Modular group algebras of totally projective $p$-primary groups. Proc. Amer. Math. Soc. 76 (1979), 31-34. MR 0534384 | Zbl 0388.20041
[M2] May W.: Modular group algebras of simply presented abelian groups. Proc. Amer. Math. Soc. 104 (1988), 403-409. MR 0962805 | Zbl 0691.20008
[M] 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. MR 0633857
[U] Ullery W.: An isomorphism theorem for commutative modular group algebras. Proc. Amer. Math. Soc. 110 (1990), 287-292. MR 1031452 | Zbl 0712.20036
[W] Warfield R.: A classification theorem for abelian $p$-groups. Trans. Amer. Math. Soc. 210 (1975), 149-168. MR 0372071 | Zbl 0324.20058
Partner of
EuDML logo