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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
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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

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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
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8. Sehgal, S.K., Topics in group rings, Marcel Dekker 1978 Google Scholar