Timeline for p-groups with isomorphic automophism groups.
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Apr 17, 2020 at 4:06 | comment | added | Joshua Grochow | @Primoz or OP - add as an answer? | |
| Jun 19, 2013 at 17:17 | comment | added | Yassine Guerboussa | @Primoz : Thank you so much. Just I note that an affirmative answer to my question follows from THEOREM 2.10. in Iyer's paper. This result is due to K. H. Hyde : "On the order of the automorphism group of a finite group, Ph.D.Thesis, University of Utah, 1969. | |
| Jun 18, 2013 at 14:23 | comment | added | Yassine Guerboussa | @ Alex Bartel : I'm sorry, for the divisibility conjecture we have to assume that our p-group has order at least p^3. This conjecture is trivially false for p-groups of order p and p^2, for the cyclic one, the automorphism groups have order p-1. and a group of order p^2 is either cyclic, so its automorphism group has order p(p-1), or is elementary abelian, so its automorphism group is Gl(2, p) which has p (p-1)^2 elements. | |
| Jun 17, 2013 at 22:34 | comment | added | Alex B. | Your divisibility conjecture is not true. The order of $C_2\times C_2$ does not divide the order of its automorphism group $\text{GL}_2(\mathbb{F}_2)\cong S_3$. | |
| Jun 17, 2013 at 21:07 | comment | added | Primoz | See H. K. Iyer, On solving the equation Aut(X)=G, Rocky Mountain Journal of Mathematics 9 (1979), no. 4, 653--670. The paper can be accessed here: projecteuclid.org/DPubS/Repository/1.0/… | |
| Jun 17, 2013 at 16:59 | comment | added | Fernando Muro | You could edit your question accordingly, adding also the reasons why you think it's true. | |
| Jun 17, 2013 at 16:43 | comment | added | Yassine Guerboussa | @Fernando Muru, I'm not sure, I just think that is true. | |
| Jun 17, 2013 at 16:27 | comment | added | Fernando Muro | Are you sure that your assertion is true? | |
| Jun 17, 2013 at 15:53 | history | asked | Yassine Guerboussa | CC BY-SA 3.0 |