Timeline for a group with all sylow p subgroups cyclic
Current License: CC BY-SA 3.0
3 events
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| Mar 26, 2013 at 7:12 | comment | added | Geoff Robinson | @Tom: Well, for example, you could get a semidirect product with a normal Sylow $31$-subgroup with a cyclic group of order $15$ acting faithfully as a group of automorphisms of the group of order $31$. In that case, the smallest prime divisor of the group order is $3,$ there is a normal $3$-complement, but that normal complement os not cyclic- it is a Frobenius group of order $155$. | |
| Mar 26, 2013 at 1:17 | comment | added | Tom | @Geoff:If both the Sylow $p$subgroup $P$ and the normal $p-$complement are cyclic,here $p$ is the smallest prime divisor of $|G|$,if we can get $C_G(P)=P$ or what will happen to $G$?And in what cases $G$ can be noncyclic? | |
| Mar 26, 2013 at 0:06 | history | answered | Geoff Robinson | CC BY-SA 3.0 |