Timeline for A question on minimal subgroups
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Jan 26, 2017 at 11:35 | comment | added | Derek Holt | Or examples of form $Z_p \rtimes Z_{q^2}$ with nontrivial action but with $Z_q$ centralizing $Z_p$. I think you could prove that $G$ either has one of a limited list of easy structures or $G$ is simple. Either $|G|=p^3$ or a Sylow $p$-subgroup of $G$ has order $p$ or $p^2$ and hence is abelian. If it is self-normalizing then you can apply Burnside's Transfer Theorem to get a normal $p$-complement. That's my contribution! | |
| Jan 26, 2017 at 11:34 | history | edited | H.Shahsavari | CC BY-SA 3.0 |
added 31 characters in body
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| Jan 26, 2017 at 11:32 | comment | added | H.Shahsavari | Oh... that's true. I forgot about it. I will update the question adding this case. | |
| Jan 26, 2017 at 11:24 | comment | added | Nick Gill | I don't think your claim is right -- what about $Z_p\times Z_{q^2}$, for $p$ and $q$ distinct primes? If you want to classify these things, I'd try and figure out the structure of the generalized Fitting group of $G$. | |
| Jan 26, 2017 at 9:52 | comment | added | H.Shahsavari | Can we claim that if $G$ is not a p-group or a Frobenius group, then it is always a simple group? | |
| Jan 26, 2017 at 9:51 | comment | added | H.Shahsavari | @Professors Holt and Gill. Can you help me to find a complete classification of such groups? | |
| Jan 26, 2017 at 9:35 | comment | added | Derek Holt | Or $Z_{31}$ in $L_5(2)$ of $Z_{127}$ in $ L_7(2)$ or $Z_{8191}$ in $L_{13}(2)$, etc., or $Z_{1093}$ in $L_7(3)$. | |
| Jan 26, 2017 at 9:28 | comment | added | Nick Gill | What about $L=Z_{13}$ inside $PSL_3(3)$? | |
| Jan 26, 2017 at 9:18 | comment | added | Geoff Robinson | This question has a strange form. You make a statement, and then ask if it is true. | |
| Jan 26, 2017 at 9:03 | history | asked | H.Shahsavari | CC BY-SA 3.0 |