群G是无限群,a是G的元,怎样证明元a的阶与其逆元的阶相等

a的阶设为n,则a^n=e,设b=a^{-1},则b^n * a^n = b...ba...a = b...(ba)...a=b...(e)...a=b^{n-1}*a^{n-1}=...=ba=e,因为a^n=e,所以b^n=e.