It is proved that among the regular polygons with prime edges, only the regular polygons with Fermat prime edges are constructable with compass and straightedge. As 17 is a Fermat prime number, the construction of hep...It is proved that among the regular polygons with prime edges, only the regular polygons with Fermat prime edges are constructable with compass and straightedge. As 17 is a Fermat prime number, the construction of heptadecagon has been discussing all the time. Many different construction methods are proposed although they are based on the same theory. Simplification of the construction is still a sensible problem. Here, we propose a simple method for constructing regular heptadecagon with the fewest steps. The accumulation of construction errors is also avoided. This method is more applicable than the previous construction.展开更多
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（2,Z_...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（2,Z_z^y） 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.展开更多
文摘It is proved that among the regular polygons with prime edges, only the regular polygons with Fermat prime edges are constructable with compass and straightedge. As 17 is a Fermat prime number, the construction of heptadecagon has been discussing all the time. Many different construction methods are proposed although they are based on the same theory. Simplification of the construction is still a sensible problem. Here, we propose a simple method for constructing regular heptadecagon with the fewest steps. The accumulation of construction errors is also avoided. This method is more applicable than the previous construction.
文摘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（2,Z_z^y） 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.
