TY - JOUR

T1 - On lie powers of regular modules in characteristic 2

AU - Kovács, L. G.

AU - Stöhr, Ralph

N1 - Publisher Copyright:
© 2004, Universita di Padova. All rights reserved.

PY - 2004

Y1 - 2004

N2 - We study Lie powers of regular modules for finite groups over a field of characteristic 2. First we prove two rather general reduction theorems, and then we apply them to Lie powers of the regular module for the Klein four group. For the latter, we solve the decomposition problem for the Lie power in degree 8, a module of dimension 8160. It has been known that of the infinitely many possible indecomposables, only four occur as direct summands in Lie powers of degree not divisible by 4, but that a fifth makes its appearance in the Lie power of degree 4. It is quite a surprise that no new indecomposables appear among the direct summands in degree 8.

AB - We study Lie powers of regular modules for finite groups over a field of characteristic 2. First we prove two rather general reduction theorems, and then we apply them to Lie powers of the regular module for the Klein four group. For the latter, we solve the decomposition problem for the Lie power in degree 8, a module of dimension 8160. It has been known that of the infinitely many possible indecomposables, only four occur as direct summands in Lie powers of degree not divisible by 4, but that a fifth makes its appearance in the Lie power of degree 4. It is quite a surprise that no new indecomposables appear among the direct summands in degree 8.

UR - http://www.scopus.com/inward/record.url?scp=38049112091&partnerID=8YFLogxK

M3 - Article

SN - 0041-8994

VL - 112

SP - 41

EP - 69

JO - Rendiconti del Seminario Matematico dell 'Universita' di Padova/Mathematical Journal of the University of Padova

JF - Rendiconti del Seminario Matematico dell 'Universita' di Padova/Mathematical Journal of the University of Padova

ER -