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…finite groups. Hence, the study and classification of finite simple groups has been one of the most fundamental problems in the theory of finite groups. For an arbitrary prime power q, the special linear group SL(2, q) consists of all the…

…invertible 2 × 2 matrices with determinant 1 over the field of q elements. The projective special linear group P SL(2, q) is defined as P SL(2, q) = SL(2, q)/Z(SL(2, q)), 1 where Z(SL(2, q)…

…76 B.10 The case for n = 7, b = 1 or b = 2 . . . . . . . . . . . . . . . . . . . . . 76 viii CHAPTER I INTRODUCTION All groups in this thesis are considered to be finite. Given a nontrivial group G, we say that a composition series for G is a…

…x28;after a possible re-ordering of the composition factors). Since every group is made up of a unique set of simple composition factors (up to isomorphism), it is understood that finite simple groups form the building blocks of all…

…x29; is the center of SL(2, q). We note that P SL(2, q) is a non-abelian simple group for a prime power q â‰¥ 4. These groups are the underlying groups at the heart of this thesis, as we now explain. In this thesis we generalize…

…8, then |G| = 168 or 360. We note that the non-abelian simple groups P SL(2, 7) and P SL(2, 9) of orders 168 and 360, respectively, satisfy the hypotheses in Theorem 7.10. The proof found in [1] and our proof of the…

…group orders given in Theorem 1.0.2 can be seen in this context. The group orders listed in the statement of this theorem correspond to the simple groups P SL(2, 7), P SL(2, 9), P SL(2, 17), P SL(2, 31), P SL…

…x28;2, 127), and P SL(2, 257), respectively. These six groups make up all of the non-abelian simple groups under consideration in this thesis. The remaining thirty-six integers given in Table 1.1 do not correspond the to the order of a non…