Some remarks on Brauer's third main theorem

Author:
Arye Juhász

Journal:
Proc. Amer. Math. Soc. **86** (1982), 363-369

MSC:
Primary 20C20

DOI:
https://doi.org/10.1090/S0002-9939-1982-0671195-9

MathSciNet review:
671195

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We consider two classes of -blocks of a finite group which have the property that for every block of them and every subgroup of , has only a small number of admissible blocks with . In this they are similar to the principal block of . These blocks are described by means of certain modules they contain.

**[1]**J. Alperin and Michel Broué,*Local methods in block theory*, Ann. of Math. (2)**110**(1979), no. 1, 143–157. MR**541333**, https://doi.org/10.2307/1971248**[2]**Richard Brauer,*Some applications of the theory of blocks of characters of finite groups. IV*, J. Algebra**17**(1971), 489–521. MR**0281806**, https://doi.org/10.1016/0021-8693(71)90006-8**[3]**Richard Brauer,*On the structure of blocks of characters of finite groups*, Proceedings of the Second International Conference on the Theory of Groups (Australian Nat. Univ., Canberra, 1973) Springer, Berlin, 1974, pp. 103–130. Lecture Notes in Math., Vol. 372. MR**0352238****[4]**R. Brauer and C. Nesbitt,*On the modular representations of finite groups*, Univ. of Toronto Studies Math. Ser. No. 4, 1937.**[5]**John Cossey and Wolfgang Gaschütz,*A note on blocks*, Proceedings of the Second International Conference on the Theory of Groups (Australian Nat. Univ. Canberra, 1973) Springer, Berlin, 1974, pp. 238–240. Lecture Notes in Math., Vol. 372. MR**0352239****[6]**Larry Dornhoff,*Group representation theory. Part A: Ordinary representation theory*, Marcel Dekker, Inc., New York, 1971. Pure and Applied Mathematics, 7. MR**0347959**

Larry Dornhoff,*Group representation theory. Part B: Modular representation theory*, Marcel Dekker, Inc., New York, 1972. Pure and Applied Mathematics, 7. MR**0347960****[7]**J. A. Green,*Blocks of modular representations*, Math. Z.**79**(1962), 100–115. MR**0141717**, https://doi.org/10.1007/BF01193108**[8]**Arye Juhász,*Variations to a theorem of H. Nagao*, J. Algebra**70**(1981), no. 1, 173–178. MR**618386**, https://doi.org/10.1016/0021-8693(81)90251-9**[9]**-,*An elementary proof to two theorems of R. Brauer*(unpublished).**[10]**-,*On the distribution of restricted modules into blocks*(submitted).**[11]**Yutaka Kawada,*On blocks of group algebras of finite groups*, Sci. Rep. Tokyo Kyoiku Daigaku Sect. A**9**(1966), 87–110 (1966). MR**0206121****[12]**D. S. Passman,*Blocks and normal subgroups*, J. Algebra**12**(1969), 569–575. MR**0242971**, https://doi.org/10.1016/0021-8693(69)90028-3

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/S0002-9939-1982-0671195-9

Keywords:
Block theory,
modules in blocks,
defect groups,
vertices

Article copyright:
© Copyright 1982
American Mathematical Society