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Michael Aschbacher 《Inventiones Mathematicae》1987,89(1):159-195
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We study the transversal spin–spin correlations in the non-equilibrium steady state of the XY chain constructed by coupling a finite cutout of the chain to the two infinite parts to its left and right acting as thermal reservoirs at different temperatures. We prove that the spatial decay of these correlations is at least exponentially fast. 相似文献
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Michael Aschbacher Michael K. Kinyon J. D. Phillips 《Transactions of the American Mathematical Society》2006,358(7):3061-3075
Bruck loops are Bol loops satisfying the automorphic inverse property. We prove a structure theorem for finite Bruck loops , showing that is essentially the direct product of a Bruck loop of odd order with a -element Bruck loop. The former class of loops is well understood. We identify the minimal obstructions to the conjecture that all finite -element Bruck loops are -loops, leaving open the question of whether such obstructions actually exist.
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Michael Aschbacher 《Journal of the American Mathematical Society》2008,21(3):809-830
We investigate the question of which finite lattices are isomorphic to the lattice of all overgroups of a subgroup in a finite group . We show that the structure of is highly restricted if is disconnected. We define the notion of a ``signalizer lattice" in and show for suitable disconnected lattices , if is minimal subject to being isomorphic to or its dual, then either is almost simple or admits a signalizer lattice isomorphic to or its dual. We use this theory to answer a question in functional analysis raised by Watatani.
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Let G be a finite alternating or symmetric group. We describe an infinite class of finite lattices, none of which is isomorphic to any interval [H,G] in the subgroup lattice of G. 相似文献
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Michael Aschbacher 《Geometriae Dedicata》1988,25(1-3):417-465
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Michael Aschbacher 《Inventiones Mathematicae》2010,180(2):225-299
We prove that if ℱ is a saturated fusion system on a finite 2-group S, then either ℱ is known, or ℱ is generated by the normalizers of two canonically defined ℱ-characteristic subgroups of S. There are various corollaries for finite groups of characteristic 2-type. 相似文献