论文信息 - Subpair multiplicities in finite groups.

Subpair multiplicities in finite groups.

The language of subpairs ([!]) provides a suitable framework for investigating connections between local and global properties of a finite group and its /-blocks (f a prime). In particular various "reduction theorems" in modular representation theory ([6], [H], [8], [4]) may be illuminated using the "local methods" introduced in [1]. On another band, R. Brauer's formulae for the lower defect group multiplicities in a finite group (see [2], [3], [9]) give strong numerical relations between the global and local invariants of a group and its blocks. It would therefore seem reasonable to try to connect these facts: this is the main purpose of this paper.

J. B. Olsson | M. Broué

[1] G. Michler,et al. Character correspondences in finite general linear, unitary and symmetric groups , 1983 .

[2] P. Fong,et al. The blocks of finite general linear and unitary groups , 1982 .

[3] Jonathan L. Alperin,et al. Local Methods in Block Theory , 1979 .

[4] M. Broué. Brauer coefficients of p-subgroups associated with a p-block of a finite group , 1979 .

[5] R. Brauer. Defect groups in the theory of representations of finite groups , 1969 .

[6] P. Fong. On the characters of $p$-solvable groups , 1961 .

[7] A. Watanabe. On generalized decomposition numbers and Fong's reductions , 1985 .

[8] L. Puig. Local block theory in p-solvable groups , 1980 .

[9] J. B. Olsson. Lower defect groups , 1980 .