The linear group SL (2, 3) as a source of examples

In introductory courses in abstract algebra the cyclic groups Z n , the dihedral groups D n , and the symmetric and alternating groups S n and A n , for various integers n , are often used to provide examples of various concepts. The intent of this note is to argue that another group could readily be added to this list: SL (2, 3), the multiplicative group of two by two invertible matrices of determinant 1 with entries from the field with three elements. Though this non-abelian group of order 24 does not appear often in introductory presentations, it is an excellent source of group theoretic examples and is also accessible to beginners, who at this stage of their study most likely have had some experience with matrices. Thus computations in SL (2, 3) can be implemented almost as easily as in the cyclic groups, and defining relations need not be introduced.