# Reference book for Suzuki groups.

I am taking a class that has a project to research one given topic. Mine is "Suzuki groups." Truth be told, I have not heard of this before in my life.

I was wondering if any of you knew a good introductory book that covers this groups. Thanks!

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You might start with the references on the Wiki Suzuki Groups. I never heard of them before. Regards –  Amzoti Jan 29 '13 at 2:58

A brief but reasonable introduction, with context provided for their place within the general classification of the finite simple groups can be found in the nice recent book,

MR2562037 (2011e:20018) Robert A. Wilson The finite simple groups Graduate Texts in Mathematics, 251. Springer-Verlag London, Ltd., London, 2009.

In particular, Chapter 4 is on Exceptional groups, and section 4.2 is on Suzuki groups.

For additional references, let me quote from Wilson's book (pg. 178):

The Suzuki groups are treated in a number of more general texts, for example Huppert and Blackburn’s ‘Finite groups. III’ (which also includes a discussion of the small Ree groups, but without proofs), and Taylor’s book ‘The geometry of classical groups’, as well as the book ‘Die Suzukigruppen und ihre Geometrien’ by Lüneburg.

(Of these, I have only seen Taylor's book. The book ends with the construction of Suzuki groups.)

For a recent result on Suzuki groups outside of the context of the classification, see this entry in Tao's blog.

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I am reading Wilson's book (mostly catching up with background), but I have a quick question. (pg 113-114) On his construction he finds some automorphism of Sp$_4(2)$ (namely, $*, e_i\leftrightarrow f_i, (4.3),$ and $(4.4)$, and then he says "these two maps generate a group of order $20$". I've been staring at it and I dont know which two automorphisms he is referring to. –  Daniel Montealegre Feb 20 '13 at 8:41