Take the tour ×

If $G$ is a finite group and $x$ is a $p'$ element of G does this imply that there a Hall $p'$ subgroup of $G$ containing $x$?

share|improve this question
No. Take $p=2$, $x=(12345)$, and $G=A_5$. It is true if $G$ is solvable. –  user641 Apr 4 '12 at 18:04
Not all groups have any Hall p-prime subgroups. A5 has no 2-prime subgroup (no subgroup of order 15) but it certainly has elements of odd order. –  Jack Schmidt Apr 4 '12 at 18:05
Thank you very much. –  user28083 Apr 4 '12 at 18:29
add comment


Your Answer



Browse other questions tagged or ask your own question.