Let $G$ be a finite group. It can be written as an unique direct sum of indecomposable groups $G_1 \times \cdots \times G_m$
Is there a method to find these groups $G_1\cdots G_m$ if I can only :
- pick a random $G$ element $g$
- given $g$, get $-g$
- given $g_1,g_2, $ get $g_1 + g_2$
Thank you for your help