On the isomorphism problem for modular group algebras of elementary abelian-by-cyclic p-groups

• Autorzy: Czesław Bagiński
• Języki publikacji: EN

Abstrakty

EN

Let G be a finite p-group and let F be the field of p elements. It is shown that if G is elementary abelian-by-cyclic then the isomorphism type of G is determined by FG.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1999
• Tom: 82
• Numer: 1
• Strony: 125-136

Daty

wydano

1999

otrzymano

1999-03-30

poprawiono

1999-06-01

Twórcy

autor

Czesław Bagiński

• Institute of Mathematics, University of Białystok, Akademicka 2, 15-267 Białystok, Poland

Bibliografia

• [1] C. Bagiński, The isomorphism question for modular group algebras of metacyclic p-groups, Proc. Amer. Math. Soc. 104 (1988), 39-42.
• [2] C. Bagiński and A. Caranti, The modular group algebras of p-groups of maximal class, Canad. J. Math. 40 (1988), 1422-1435.
• [3] B. Huppert, Endliche Gruppen I, Springer, Berlin, 1983.
• [4] R. Sandling, Units in the modular group algebra of a finite abelian p-group, J. Pure Appl. Algebra 33 (1984), 337-346.
• [5] R. Sandling, The isomorphism problem for group rings: A survey, in: Lecture Notes in Math. 1142, Springer, Berlin, 1985, 256-288.
• [6] R. Sandling, The modular group algebra of a central-elementary-by-abelian p-group, Arch. Math. (Basel) 52 (1989), 22-27.
• [7] R. Sandling, The modular group algebra problem for small p-groups of maximal class, Canad. J. Math. 48 (1996), 1064-1078.
• [8] S. Sehgal, Topics in Group Rings, Pure Appl. Math. 50, Marcel Dekker, New York, 1978.
• [9] U. H. M. Webb, An elementary proof of Gaschütz' theorem, Arch. Math. (Basel) 35 (1980), 23-26.
• [10] M. Wursthorn, Isomorphism of modular group algebras: An algorithm and its application to groups of order $2^6$, J. Symbolic Comput. 15 (1993), 211-227.