Browsing College of Science by Author "Park, Sejong"
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Analogues of Goldschmidt's thesis for fusion systems
Park, Sejong (Elsevier, 20101215)We extend the results of David Goldschmidt's thesis concerning fusion in finite groups to saturated fusion systems and to all primes. 
Control of transfer and weak closure in fusion systems
Park, Sejong (2010)We show that K¿ and K¿ control transfer in every fusion system on a finite pgroup when p ¿ 5, and that they control weak closure of elements in every fusion system on a finite pgroup when p ¿ 3. This generalizes resultsof ... 
Glauberman's and Thompson's theorems for fusion systems
Park, Sejong (American Mathematical Society, 200902)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
Park, Sejong (2010)We answer the gluing problem of blocks of finite groups (Linckelmann (2004) [7, 4.2]) for tame blocks and the principal pblock 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 RuizViruel exotic fusion systems
Park, Sejong (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
Park, Sejong (Elsevier, 201111)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
Park, Sejong (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
Park, Sejong (201003)We prove analogues of results of Tate and Yoshida on control of transfer for fusion systems. This requires the notions of pgroup residuals and transfer maps in cohomology for fusion systems. As a corollary, we obtain a ... 
The weighted fusion category algebra and the $q$Schur algebra for $\rm GL_2(q)$
Park, Sejong (ScienceDirect, 200801)[no abstract available]