Timeline for Realizable Order Sequences for Finite Groups
Current License: CC BY-SA 3.0
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
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| Sep 28, 2012 at 15:22 | comment | added | Benjamin Dickman | Thanks for the note, example, and link. It's interesting that of the five groups of order $27$, there is of course the cyclic group $C_{27}$, and then not only do $UT(3,3)$ and $C_{3}^{3}$ have the same order sequence, but so do the other two groups of this order: namely, the direct product of $C_9$ and $C_3$ as well as the semidirect product of $C_9$ and $C_3$. From these examples alone, a whole host of possible conjectures on order sequences can be dismissed outright... | |
| Sep 28, 2012 at 6:18 | comment | added | Geoff Robinson | Yes, indeed there are many non-isomorphic examples of $p$-groups of exponent $p,$ each pair providing a counterexample to the assertion that order sequence determines the isomorphism type of the group | |
| Sep 27, 2012 at 12:20 | history | answered | Denis Serre | CC BY-SA 3.0 |