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The Modular Group Algebras of P-Groups of Maximal Class

Published online by Cambridge University Press:  20 November 2018

C. Bagiński  and
A. Caranti
C. Bagiński
Affiliation:
Warsaw University, Biaiystok, Poland
A. Caranti
Affiliation:
Università degli Studi di Trento, Povo, Italy
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The isomorphism problem for modular group algebras of finite p-groups appears to be still far from a solution (see [7] for a survey of the existing results). It is therefore of interest to investigate the problem for special classes of groups.

The groups we consider here are the p-groups of maximal class, which were extensively studied by Blackburn [1]. In this paper we solve the modular isomorphism problem for such groups of order not larger than pp+1, having an abelian maximal subgroup, for odd primes p.

What we in fact do is to generalize methods used by Passman [5] to solve the isomorphism problem for groups of order p4. In Passman's paper the case of groups of maximal class is actually the most difficult one.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 40 , Issue 6 , 01 December 1988 , pp. 1422 - 1435
Copyright
Copyright © Canadian Mathematical Society 1988

References

1. Blackburn, N., On a special class of p-groups, Acta Math. 100 (1958), 45–92.Google Scholar
2. Carlson, J., Periodic modules over modular group algebras, J. London Math. Soc. 75 (1977), 431–436.Google Scholar
3. Huppert, B., Endliche Gruppen I (Springer, Berlin, 1967).CrossRefGoogle Scholar
4. Parmenter, M. M. and Milies, C. Polcino, A note on isomorphic group rings, Bol. Soc. Bras. Mat. 12 (1981), 57–59.Google Scholar
5. Passman, D, The group algebras of groups of order p4 over a modular field, Michigan Math. J. 12 (1965), 405–415.Google Scholar
6. Passman, D, Algebraic structure of group rings (Interscience, New York, 1977).Google Scholar
7. Sandling, R., The isomorphism problem for group rings: a survey, Lecture Notes in Mathematics 1142 (Springer, Berlin, 1985), 256–288.Google Scholar
8. Sehgal, S. K., On the isomorphism of group algebras, Math. Z. 95 (1967), 71–75.Google Scholar
9. Sehgal, S. K., Topics in group rings (Dekker, New York, 1978).Google Scholar