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3. Recognizing the characteristic of a simple group of Lie type from its Probabilistic Zeta function

Author

Massimiliano Patassini

Subjects
Finite group, Algebra and Number Theory, Outer automorphism group, Alternating group, Characteristic, Probabilistic Zeta function, Simple groups, Combinatorics, Algebra, Groups of Lie type, Matrix group, Group of Lie type, Symmetric group, Unitary group, Simple group, Mathematics
Abstract

We find a method to recognize the characteristic of a simple group of Lie type G from its Dirichlet polynomial P G ( s ) . This is enough to complete the proof of the following statement: if G is a simple group, H is a finite group and P G ( s ) = P H ( s ) , then H / Frat ( H ) ≅ G .

Published
2011
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