Browsing Mathematics (Scholarly Articles) by Subject "Fusion systems"
Now showing items 1-7 of 7
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Analogues of Goldschmidt's thesis for fusion systems
(Elsevier, 2010-12-15)We extend the results of David Goldschmidt's thesis concerning fusion in finite groups to saturated fusion systems and to all primes. -
Glauberman's and Thompson's theorems for fusion systems
(American Mathematical Society, 2009-02)We prove analogues of results of Glauberman and Thompson for fusion systems. As a corollary, we obtain a stronger form of Frobenius' theorem for fusion systems, applicable under the above assumptions and generalizing another ... -
The gluing problem for some block fusion systems
(2010)We answer the gluing problem of blocks of finite groups (Linckelmann (2004) [7, 4.2]) for tame blocks and the principal p-block of PSL 3 ( p ) for p odd. In particular, we show that the gluing problem for the principal ... -
Minimal characteristic bisets and finite groups realizing Ruiz-Viruel exotic fusion systems
(Elsevier, 2011)Continuing our previous work (Park, 2010) [2], we determine a minimal left characteristic biset X for every exotic fusion system FF on the extraspecial group S of order 73 and exponent 7 discovered by Ruiz and Viruel (2004) ... -
On the composition product of saturated fusion systems
(Elsevier, 2011-11)We say that a fusion system is the composition product of two subsystems if every morphism can be factored as a morphism in one fusion system followed by a morphism in the other. We establish a relationship between the ... -
Realizing a fusion system by a single finite group
(2010)We show that every saturated fusion system can be realized as a full subcategory of the fusion system of a finite group. The result suggests the definition of an 'exoticity index' and raises some other questions which we discuss. -
Tate's and Yoshida's theorems on control of transfer for fusion systems
(2010-03)We prove analogues of results of Tate and Yoshida on control of transfer for fusion systems. This requires the notions of p-group residuals and transfer maps in cohomology for fusion systems. As a corollary, we obtain a ...