Zobrazeno 1 - 10
of 157
pro vyhledávání: '"OLIVER, BOB"'
For a prime $p$, fusion systems over discrete $p$-toral groups are categories that model and generalize the $p$-local structure of Lie groups and certain other infinite groups in the same way that fusion systems over finite $p$-groups model and gener
Externí odkaz:
http://arxiv.org/abs/2409.09703
Autor:
Oliver, Bob
We correct an error in Lemma 3.1 of my paper coauthored with Ran Levi on the Benson-Solomon fusion systems, and show that the change does not affect any of the other results in that paper. More precisely, as pointed out to us by Justin Lynd, there ar
Externí odkaz:
http://arxiv.org/abs/2303.12844
Autor:
Oliver, Bob
For a finite abelian $p$-group $A$ and a subgroup $\Gamma\le\text{Aut}(A)$, we say that the pair $(\Gamma,A)$ is fusion realizable if there is a saturated fusion system $\mathcal{F}$ over a finite $p$-group $S\ge A$ such that $C_S(A)=A$, $\textrm{Aut
Externí odkaz:
http://arxiv.org/abs/2209.15375
Autor:
Oliver, Bob
We study a certain family of simple fusion systems over finite $3$-groups, ones that involve Todd modules of the Mathieu groups $2M_{12}$, $M_{11}$, and $A_6=O^2(M_{10})$ over $\mathbb{F}_3$, and show that they are all isomorphic to the $3$-fusion sy
Externí odkaz:
http://arxiv.org/abs/2204.07750
Autor:
Oliver, Bob
We describe some new ways to construct saturated fusion subsystems, including, as a special case, the normalizer of a set of components of the ambient fusion system. This was motivated in part by Aschbacher's construction of the normalizer of one com
Externí odkaz:
http://arxiv.org/abs/2107.09494
Autor:
Oliver, Bob
Publikováno v:
Fundamenta math. 259 (2022), 287-312
We prove that the factorization of a saturated fusion system over a discrete $p$-toral group as a product of indecomposable subsystems is unique up to normal automorphisms of the fusion system and permutations of the factors. In particular, if the fu
Externí odkaz:
http://arxiv.org/abs/2103.11158
A saturated fusion system over a finite $p$-group $S$ is a category whose objects are the subgroups of $S$ and whose morphisms are injective homomorphisms between the subgroups satisfying certain axioms. A fusion system over $S$ is realized by a fini
Externí odkaz:
http://arxiv.org/abs/2102.08278
Autor:
Oliver, Bob
We fill in a gap in the proof of the main theorem in our earlier paper [Ol]. At the same time, we prove a slightly stronger version of the theorem needed for another paper.
Externí odkaz:
http://arxiv.org/abs/2102.00794
Autor:
Oliver, Bob, Ruiz, Albert
Publikováno v:
Transactions Amer. Math. Soc. 374 (2021), 7743-7777
We determine for which known finite simple groups $G$ and which primes $p$ the $p$-fusion system of $G$ is simple. This means first collecting together the results that were already known (and correcting two errors made in an earlier study of this qu
Externí odkaz:
http://arxiv.org/abs/2007.07578
Publikováno v:
Ann. K-Th. 6 (2021) 425-480
In a 2009 paper, Dave Benson gave a description in purely algebraic terms of the mod $p$ homology of $\Omega(BG^\wedge_p)$, when $G$ is a finite group, $BG^\wedge_p$ is the $p$-completion of its classifying space, and $\Omega(BG^\wedge_p)$ is the loo
Externí odkaz:
http://arxiv.org/abs/1807.02353