Abstract
In this chapter we describe the six families of so-called ‘classical’ simple groups. These are the linear, unitary and symplectic groups, and the three families of orthogonal groups. All may be obtained from suitable matrix groups G by taking G′/Z(G′). Our main aims again are to define these groups, prove they are simple, and describe their automorphisms, subgroups and covering groups.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2009 Springer-Verlag London Limited
About this chapter
Cite this chapter
Wilson, R.A. (2009). The classical groups. In: The Finite Simple Groups. Graduate Texts in Mathematics, vol 251. Springer, London. https://doi.org/10.1007/978-1-84800-988-2_3
Download citation
DOI: https://doi.org/10.1007/978-1-84800-988-2_3
Publisher Name: Springer, London
Print ISBN: 978-1-84800-987-5
Online ISBN: 978-1-84800-988-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)