The distribution of modular representations into blocks

Author:
David W. Burry

Journal:
Proc. Amer. Math. Soc. **78** (1980), 14-16

MSC:
Primary 20C20

MathSciNet review:
548074

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The *p*-modular representations of a finite group that are induced from a *p*-subgroup are investigated. A series of three results describing how these representations are distributed into *p*-blocks are presented. Several applications are discussed, including the result that there are a finite number of indecomposable *p*-modular representations (up to equivalence) in a *p*-block of a group if and only if its defect group is cyclic.

**[1]**David W. Burry,*A strengthened theory of vertices and sources*, J. Algebra**59**(1979), no. 2, 330–344. MR**543254**, 10.1016/0021-8693(79)90131-5**[2]**Larry Dornhoff,*Group representation theory. Part B: Modular representation theory*, Marcel Dekker, Inc., New York, 1972. Pure and Applied Mathematics, 7. MR**0347960****[3]**Wolfgang Hamernik,*Indecomposable modules with cyclic vertex*, Math. Z.**142**(1975), 87–90. MR**0364413****[4]**D. G. Higman,*Indecomposable representations at characteristic 𝑝*, Duke Math. J.**21**(1954), 377–381. MR**0067896****[5]**Jean-Pierre Serre,*Linear representations of finite groups*, Springer-Verlag, New York-Heidelberg, 1977. Translated from the second French edition by Leonard L. Scott; Graduate Texts in Mathematics, Vol. 42. MR**0450380**

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

Retrieve articles in all journals with MSC: 20C20

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1980-0548074-9

Keywords:
Induced module,
block,
defect group,
source

Article copyright:
© Copyright 1980
American Mathematical Society