TITLE: Loop space homology associated to the mod 2 Dickson invariants}

AUTHORS: 
Ran Levi, 
Institute of Mathematics, University of Aberdeen, Aberdeen AB24 3UE, U.K.}


Nora Seeliger
LAGA, Institut Galilee, Av. J-B Clement, 93430
Villetaneuse, France


AMS CLASSIFICATION: Primary 55R35. Secondary 55R40, 20D20

arXiv:1001.3581v1

ABSTRACT
The spaces BG_2 and BDI(4) have the property that their mod 2 cohomology is given by the rank 3 and 4 Dickson invariants respectively. Associated with these spaces one has for q odd the classifying spaces of the finite groups BG_2(q)and the exotic family of classifying spaces of 2-local finite groups BSol(q). In this article compute the mod 2 loop space homology of the 2-completed classifying space of G_2(q) and  of BSol(q) for all odd primes q, as algebras over the Steenrod algebra, and the associated Bockstein spectral sequences.