Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Modular group algebras of totally projective $ p$-primary groups


Author: Warren May
Journal: Proc. Amer. Math. Soc. 76 (1979), 31-34
MSC: Primary 20C20; Secondary 20C30
DOI: https://doi.org/10.1090/S0002-9939-1979-0534384-X
MathSciNet review: 534384
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let F be a field of characteristic $ p > 0$ and let G be a totally projective abelian p-group of countable p-length. If $ FG \cong FH$ for some group H, then it is shown that $ G \cong H$.


References [Enhancements On Off] (What's this?)

  • [1] S. D. Berman and T. Zh. Mollov, The group rings of abelian p-groups of arbitrary power (Russian), Mat. Zametki 6 (1969), 381-392; Math. Notes 6 (1969), 686-692. MR 40 #7365. MR 0254155 (40:7365)
  • [2] P. F. Dubois and S. K. Sehgal, Another proof of the invariance of Ulm's functions in commutative modular group rings, Math. J. Okayama Univ. 15 (1972), 137-139. MR 47 #6892. MR 0318345 (47:6892)
  • [3] L. Fuchs, Infinite abelian groups, vol. II, Academic Press, New York, 1973. MR 0349869 (50:2362)
  • [4] P. Hill, Isotype subgroups of direct sums of countable groups, Illinois J. Math. 13 (1969), 281-290. MR 39 #1550. MR 0240198 (39:1550)
  • [5] W. May, Commutative group algebras, Trans. Amer. Math. Soc. 136 (1969), 139-149. MR 38 #2224. MR 0233903 (38:2224)
  • [6] T. Zh. Mollov, The multiplicative groups of modular group algebras of primary abelian groups of arbitrary cardinality. I (Russian), Publ. Math. Debrecen 18 (1971), 9-21 (1972). MR 47 #341; II (Russian), ibid. 19 (1972), 87-96 (1973). MR 49 #2980. MR 0311779 (47:341)
  • [7] -, Sylow p-subgroups of group algebras of countable abelian groups (Russian), C. R. Acad. Bulgare Sci. 27 (1974), 733-735. MR 51 #5805. MR 0369572 (51:5805)
  • [8] D. S. Passman, Advances in group rings, Israel J. Math. 19 (1974), 67-107. MR 50 #9945. MR 0357477 (50:9945)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 20C20, 20C30

Retrieve articles in all journals with MSC: 20C20, 20C30


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1979-0534384-X
Keywords: Totally projective p-groups, modular group algebras
Article copyright: © Copyright 1979 American Mathematical Society

American Mathematical Society