Timeline for Infinite finitely generated groups whose Frattini factors are Klein 4-group
Current License: CC BY-SA 3.0
10 events
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Jan 14, 2017 at 13:20 | comment | added | Alireza Abdollahi | @AndreiJaikin I wish he can put his answer himself here! This answers (Problem 17.17 of THE KOUROVKA NOTEBOOK, No. 18; arxiv.org/pdf/1401.0300v8.pdf) proposed by G.M.Bergman: If a finitely generated group $G$ has $n < \infty$ maximal subgroups, must $G$ be finite? In particular, what if $n = 3$? | |
Jan 14, 2017 at 13:13 | comment | added | Alireza Abdollahi | @AndreiJaikin. Andrei Jaikin-Zapirain has sent an answer in Group-Pub-forum at 2016/Aug/21 as follows: An example of an infinite group with 3 maximal subgroups can be extracted from the paper Ershov, Mikhail; Jaikin-Zapirain, Andrei Groups of positive weighted deficiency and their applications. J. Reine Angew. Math. 677 (2013), 71–134. A 2-generated 2-LERF group (see Section 7 of the paper) has this property because its maximal subgroups have index 2. | |
Feb 26, 2016 at 19:12 | comment | added | Alireza Abdollahi | @GeoffRobinson. Actually it is equivalent to ask if there is an infinite finitely generated group with exactly 3 maximal subgroups (without any other restriction on the indices). | |
Feb 25, 2016 at 0:54 | comment | added | Geoff Robinson | I think an equivalent form of the question is whether there can be an infinite group $G$ which has exactly three maximal subgroups each of index $2$ ( if there is such a $G$, it must be generated by two elements). | |
Feb 20, 2016 at 13:41 | review | Low quality posts | |||
Feb 20, 2016 at 13:53 | |||||
Feb 20, 2016 at 13:41 | history | edited | Alireza Abdollahi | CC BY-SA 3.0 |
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Feb 20, 2016 at 13:39 | comment | added | Alireza Abdollahi | @HJRW. I mean the quotient by the Frattini subgroup. | |
Feb 20, 2016 at 13:35 | comment | added | HJRW | By Frattini factor, do you mean its Frattini subgroup or the quotient by the Frattini subgroup? Or something else? | |
Feb 20, 2016 at 13:21 | review | Low quality posts | |||
Feb 20, 2016 at 13:24 | |||||
Feb 20, 2016 at 13:03 | history | asked | Alireza Abdollahi | CC BY-SA 3.0 |