Another Uniqueness Proof of the Dickson Simple Group G(2)(3)

作者：Michler Gerhard O; Wang Lizhong^*

来源：Algebra Colloquium, 2011, 18(2): 181-210.

DOI：10.1142/s1005386711000125

• Dickson simple group G(2)(3)
• ordinary representations

In this article, we give a self-contained uniqueness proof for the Dickson simple group G = G(2)(3) using the first author's uniqueness criterion. The uniqueness proof for G(2)(3) was first given by Janko. His proof depends on Thompson's deep and technical characterization of G(2)(3).
Let H' be the amalgamated central product of SL2(3) with itself. Then there is a unique extension H of H' by a cyclic group of order 2 such that H has a center of order 2 and both factors SL2(3) are normal in H. We prove that any simple group G having a 2-central involution z with centralizer C-G(z) congruent to H is isomorphic to G(2)(3).

• 出版日期2011-6
• 单位北京大学