Timeline for Central frattini extensions
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
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| Jun 19, 2013 at 17:02 | comment | added | Yassine Guerboussa | in the first line of the above comment, I mean "...exponent at most $p^{sc}$". | |
| Jun 19, 2013 at 16:58 | comment | added | Yassine Guerboussa | Ok, I think that I have an answer. A p-group G in the class V has exponent at most p^s. Also if $Z(G) \leq \Phi (G)$ then d(G) the minimal number of generators of G equals to $d=d(G/Z(G)$, and by a nice result of Thompson (A. Mann for 2-groups), d can not exceed $t(t+1)/2$. It follows from Zelmanov solution of the restricted Burnside problem that V contains only finitely many p-groups with a center contained in the frattini subgroup. Also It seems to me that a variation of the above argument answers the first question negatively. | |
| Jun 17, 2013 at 13:40 | history | asked | Yassine Guerboussa | CC BY-SA 3.0 |