The projective representations types of finite groups over a ring of formal power series

• Autorzy: Klein D.
• Języki publikacji: EN

Abstrakty

EN

Let F be a field of characteristic p >0,S=F[[X]],S^∗ the unit group of S, and W a subgroup of S ^∗. We characterize finite groups depending on a projective (S,W)-representation type. We also give necessary and sufficient conditions for a finite group and its Sylow p-subgroups to be of the same projective (S,W) -representation type.

Słowa kluczowe

EN

algebra; integrals; finite groups

PL

algebra; całki; grupy skończone

• Wydawca: Wydawnictwo Uniwersytetu Humanistyczno-Przyrodniczego im. Jana Długosza w Częstochowie
• Czasopismo: Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
• Rocznik: 2009
• Tom: Vol. 14
• Strony: 63--73
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Klein D.

• Institute of Mathematics Pomeranian University of Słupsk Arciszewskiego 22b, 76-200 Słupsk, Poland

Bibliografia

• [1] I. Assem, D. Simson, A. Skowroński. Elements of the Representation Theory of Associative Algebras. Vol. 1. Techniques of Representation Theory. London Math. Soc. Stud. Texts, vol. 65, Cambridge Univ.Press, Cambridge 2006.
• [2] A.F. Barannyk, P.M. Gudyvok. On the algebra of projective integral representations of finite groups. Dopov. Akad. Nauk Ukr. RSR, Ser. A,291-293, 1972. (In Ukrainian).
• [3] L.F. Barannyk, D. Klein. Twisted group rings of strongly unbounded representation type. Colloq. Math.100, 265-287, 2004.
• [4] L.F. Barannyk, K. Sobolewska. On indecomposable projective representations of finite groups over fields of characteristic p>0.Colloq.Math.98, 171-187, 2003.
• [5] C.W. Curtis, I. Reiner. Representation Theory of Finite Groups and Associative Algebras. Interscience, New York 1962 (2nd ed., 1966).
• [6] C.W Curtis, I. Reiner. Methods of Representation Theory with Applications to Finite Groups and Orders, Vol. 1 , Wiley, New York 1981.
• [7] W. Gaschütz Über den Fundamentalsatz von Maschke zur Darstel-lungstheorie der endlichen Gruppen.Math. Z.56 , 376-387, 1952.
• [8] P.M Gudyvok. On boundedness of degrees of indecomposable modular representations of finite groups over principal ideal rings .Dopov. Akad. Nauk Ukr. RSR, Ser. A, 683-685, 1971. (In Ukrainian).
• [9] G. Karpilovsky. Group Representations , Vol. 2. North-Holland Math. Stud. 177, North-Holland, Amsterdam 1993.