Voir la notice de l'article provenant de la source Annals of Mathematics website
We extend the notion of a $p$-local finite group (defined in [BLO03]) to the notion of a $p$-local group. We define morphisms of $p$-local groups, obtaining thereby a category, and we introduce the notion of a representation of a $p$-local group via signalizer functors associated with groups. We construct a chain $\mathfrak{G}=(\mathcal{G}_0\to\mathcal{G}_1\to\cdots)$ of $2$-local finite groups, via a representation of a chain $\frak G^*=(G_0\to G_1\to\cdots)$ of groups, such that $\mathcal{G}_0$ is the $2$-local finite group of the third Conway sporadic group ${\rm Co}_3$, and for $n>0$, $\mathcal{G}_n$ is one of the $2$-local finite groups constructed by Levi and Oliver in [LO02]. We show that the direct limit $\mathcal{G}$ of $\mathfrak{G}$ exists in the category of $2$-local groups, and that it is the $2$-local group of the union of the chain $\mathfrak{G}^*$. The $2$-completed classifying space of $\mathcal{G}$ is shown to be the classifying space $B\operatorname{D}\operatorname{I}(4)$ of the exotic $2$-compact group of Dwyer and Wilkerson [DW93].
Michael Aschbacher 1 ; Andrew Chermak 2
@article{10_4007_annals_2010_171_881,
author = {Michael Aschbacher and Andrew Chermak},
title = {A group-theoretic approach to a family of $2$-local finite groups constructed by {Levi} and {Oliver}},
journal = {Annals of mathematics},
pages = {881--978},
publisher = {mathdoc},
volume = {171},
number = {2},
year = {2010},
doi = {10.4007/annals.2010.171.881},
mrnumber = {2630058},
zbl = {1213.20017},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2010.171.881/}
}
TY - JOUR AU - Michael Aschbacher AU - Andrew Chermak TI - A group-theoretic approach to a family of $2$-local finite groups constructed by Levi and Oliver JO - Annals of mathematics PY - 2010 SP - 881 EP - 978 VL - 171 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4007/annals.2010.171.881/ DO - 10.4007/annals.2010.171.881 LA - en ID - 10_4007_annals_2010_171_881 ER -
%0 Journal Article %A Michael Aschbacher %A Andrew Chermak %T A group-theoretic approach to a family of $2$-local finite groups constructed by Levi and Oliver %J Annals of mathematics %D 2010 %P 881-978 %V 171 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4007/annals.2010.171.881/ %R 10.4007/annals.2010.171.881 %G en %F 10_4007_annals_2010_171_881
Michael Aschbacher; Andrew Chermak. A group-theoretic approach to a family of $2$-local finite groups constructed by Levi and Oliver. Annals of mathematics, Tome 171 (2010) no. 2, pp. 881-978. doi: 10.4007/annals.2010.171.881
Cité par Sources :