Modular group algebras of 𝑁-groups

Ullery, William

doi:10.1090/S0002-9939-1988-0954982-4

Modular group algebras of $N$-groups
HTML articles powered by AMS MathViewer

by William Ullery

Proc. Amer. Math. Soc. 103 (1988), 1053-1057

DOI: https://doi.org/10.1090/S0002-9939-1988-0954982-4

PDF | Request permission

Abstract:

For a prime $p$, let $F$ be the field with $p$ elements and let $G$ be a reduced $p$-primary abelian $N$-group. If $FG \cong FH$ for some group $H$, then it is shown that $G \cong H$.

References

S. D. Berman and T. Ž. Mollov, The group rings of abelian $p$-groups of arbitrary power, Mat. Zametki 6 (1969), 381–392 (Russian). MR 254155
Donna Beers, Fred Richman, and Elbert A. Walker, Group algebras of abelian groups, Rend. Sem. Mat. Univ. Padova 69 (1983), 41–50. MR 716984
Paul F. Dubois and Sudarshan K. Sehgal, Another proof of the invariance of Ulm’s functions in commutative modular group rings, Math. J. Okayama Univ. 15 (1971/72), 137–139. MR 318345
László Fuchs, Infinite abelian groups. Vol. I, Pure and Applied Mathematics, Vol. 36, Academic Press, New York-London, 1970. MR 0255673
Paul Hill, The classification of $N$-groups, Houston J. Math. 10 (1984), no. 1, 43–55. MR 736574
Warren May, Commutative group algebras, Trans. Amer. Math. Soc. 136 (1969), 139–149. MR 233903, DOI 10.1090/S0002-9947-1969-0233903-9
Warren May, Modular group algebras of totally projective $p$-primary groups, Proc. Amer. Math. Soc. 76 (1979), no. 1, 31–34. MR 534384, DOI 10.1090/S0002-9939-1979-0534384-X

Modular group algebras of simply presented abelian groups