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 \(GL\left( {2,{Z_{{z^\lambda }}}} \right)\) 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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Biography: HUANG Benwen, male, Professor, research direction:finite group.
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Huang, B., Zhang, L. & Wu, X. Properties of a class of groups on Z m . Wuhan Univ. J. Nat. Sci. 22, 5–12 (2017). https://doi.org/10.1007/s11859-017-1210-0
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DOI: https://doi.org/10.1007/s11859-017-1210-0