Properties of a class of groups on Zm |
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Authors: | Benwen Huang Li Zhang Xiaotao Wu |
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Affiliation: | 1.City College,Wuhan University of Science and Technology,Hubei,China |
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Abstract: | In this paper, we obtain the factorization of direct production and order of group GL(n, Z m ) in a simple method. Then we generalize some properties of GL(2, Z p ) proposed by Huppert, and prove that the group (GLleft( {2,{Z_{{z^lambda }}}} right)) is solvable. We also prove that group GL(n, Z p ) is solvable if and only if GL(n, Z p ) is solvable, and list the generators of groups GL(n, Z p ) and SL(n, Z p ). At last, we prove that PSL(2, Z p )(p > 3) and PSL(n, Z p )(n > 3) are simple. |
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