Hostname: page-component-848d4c4894-ndmmz Total loading time: 0 Render date: 2024-05-13T11:18:50.881Z Has data issue: false hasContentIssue false
  • English
  • Français

On Automorphisms of Complete Algebras And The Isomorphism Problem for Modular Group Rings

Published online by Cambridge University Press:  20 November 2018

Frank Röhl
Frank Röhl*
Affiliation:
Department of Mathematics The University of Alabama Tuscaloosa, Al 35487, USA
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In [5], Roggenkamp and Scott gave an affirmative answer to the isomorphism problem for integral group rings of finite p-groups G and H, i.e. to the question whether ZG ⥲ ZH implies G ⥲ H (in this case, G is said to be characterized by its integral group ring). Progress on the analogous question with Z replaced by the field Fp of p elements has been very little during the last couple of years; and the most far reaching result in this area in a certain sense - due to Passi and Sehgal, see [8] - may be compared to the integral case, where the group G is of nilpotency class 2.

Keywords

16A2720C07
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 42 , Issue 3 , 01 June 1990 , pp. 383 - 394
Copyright
Copyright © Canadian Mathematical Society 1990

References

1. Huppert, B. and Blackburn, N., Finite groups I I, Springer 1982 Google Scholar
2. NĂstĂsescu, C. and Oystayen, F. van, Graded ring theory, North-Holland 1982 Google Scholar
3. Neumann, H., Varieties of groups, Springer 1967 Google Scholar
4. Passi, I.B.S., Group rings and their augmentation ideals, Springer LNM 715, 1979Google Scholar
5. Roggenkamp, K.W. and Scott, L., Isomorphisms of p-adic group rings, Ann. Math. 126 (1987), 593–64.Google Scholar
6. Röhl, F., On the isomorphism problem for group rings and completed augmentation ideals, Rocky Mountain J. Math. 17, No 4 (1987), 853–86.Google Scholar
7. Sandling, R., The isomorphism problem for group rings: a survey in Orders and their applications, Springer LNM 1142, 1985 Google Scholar
8. Sehgal, S.K., Topics in group rings, Marcel Dekker 1978 Google Scholar