Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A criterion for finite module type

Author: Christine Bessenrodt
Journal: Proc. Amer. Math. Soc. 85 (1982), 520-522
MSC: Primary 20C20
MathSciNet review: 660595
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The following result is proved: If a $ p$-block of a finite group has only finitely many indecomposable liftable modules with the defect group of the block as a vertex or if it has only finitely many indecomposable periodic modules, then the block is of finite module type.

References [Enhancements On Off] (What's this?)

  • [1] J. L. Alperin, Periodicity in groups, Illinois J. Math. 21 (1977), 776-783. MR 0450381 (56:8676)
  • [2] D. W. Burry, The distribution of modular representations into blocks, Proc. Amer. Math. Soc. 78 (1980), 14-16. MR 548074 (80j:20010)
  • [3] L. Dornhoff, Group representation theory B, Marcel Dekker, New York, 1971. MR 0347959 (50:458a)
  • [4] J. A. Green, Vorlesungen über modulare Darstellungstheorie endlicher Gruppen, Vorlesungen aus dem Math. Institut Giessen, 1974. MR 0360788 (50:13235)
  • [5] W. Hamernik, Indecomposable modules with cyclic vertex, Math. Z. 142 (1975), 87-90. MR 0364413 (51:667)
  • [6] A. Heller, Indecomposable representations and the loop space operation, Proc. Amer. Math. Soc. 12 (1961), 640-643. MR 0126480 (23:A3776)
  • [7] R. M. Peacock, Ordinary character theory in a block with a cyclic defect group, J. Algebra 44 (1977), 203-220. MR 0424922 (54:12880)
  • [8] L. L. Scott, Modular permutation representations, Trans. Amer. Math. Soc. 175 (1973), 101-122. MR 0310051 (46:9154)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 20C20

Retrieve articles in all journals with MSC: 20C20

Additional Information

Keywords: Block, liftable module, periodic module, defect group, vertex
Article copyright: © Copyright 1982 American Mathematical Society

American Mathematical Society