let $P_1$, $P_2$ be two different Sylow p-subgroups of $G$.
is this possible that non-identity element $a$ is in both $P_1$, $P_2$?
I thought this would be proved easily but I don't know even how to start.
hints or ideas?
2026-03-28 16:12:42.1774714362
common elements in two Sylow p-subgroups?
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Yes, this happens for example for $p=2$ in the group $S_4$ as can be seen either directly or by considering the number of elements in a product of two different $2$-Sylow subgroups.