【摘要】 设f:G→G是群G的自同态,满足f(x)=xn(x∈G),证明了G是交换群当且仅当n=-1或2;设M={n|f:G→G是群G的自同态,满足f(x)=xn,x∈G},证明了G是交换群当且仅当n遍历M中所有元时,所有形如n(n-1)元的最大公因数为2.更多还原

【Abstract】 Let f:G→G be an homomorphism of a group G,satisfying f(x) = xn(x∈G),prove that G is commutative if and only if n =- 1 or 2.Let M = { n | f:G→G is homomorphism of G,satisfying f(x) = xn,x∈G} prove that G is commutative if and only if the greatest common multiples of numbers of the form of n(n- 1),when n is running over the set M,is 2.更多还原