Talk:Burnside problem

message: I don't think the linked article defines the p∞-group. Cound someone do that here? Orthografer 23:16, 21 October 2006 (UTC)
replies: text: I've corrected the link: p∞-groups are also called Prüfer groups (or quasicyclic groups). --Zundark 10:35, 22 October 2006 (UTC)
thread_title:  [[p-group|''p''<sup>∞</sup>-group]] 

message: A recent addition claims that the free Burnside group of rank 2 and exponent 5 has been proven infinite. The only reference is to an arxiv paper, 1105.0847v2, by Heikki Koivupalo and Kazuma Morita. Even setting aside whether such a reference would suffice, I find no paper in the arxiv with Koivupalo as an author. Paper 1105.0847 is written by Kazuma Morita alone, is in the Number Theory section, and is titled Generalization of the theory of Sen in the semi-stable representation case . I cannot find the word "Burnside" in that paper. Unless someone objects, I am reverting that addition. Magidin (talk) 19:19, 31 May 2011 (UTC)
thread_title:  Recent addition about B(2,5) 

message: In the section "Bounded Burnside problem" there is the following claim: "In the case of the odd exponent, all finite subgroups of the free Burnside groups were shown to be cyclic groups." Could someone provide a reference for that claim? In the book "The Burnside Problem and Identities in Groups" by Adjan I could only find Theorem 3.3 (on page 261), which states that this is only true if we assume that the finite subgroup is also abelian.  — Preceding unsigned comment added by CGHaus (talk • contribs) 14:32, 9 October 2014 (UTC)
thread_title:  Finite Subgroups of free Burnside group 

message: https://books.google.hu/books?id=OaNsCQAAQBAJ&pg=PA21&lpg=PA21&dq=o+yu+schmidt+problem&source=bl&ots=P8b7f_mS-C&sig=lz6NIDDuhEX89ztYt1oEqvHEp2Y&hl=en&sa=X&ved=0CD0Q6AEwCWoVChMIl9_yrpDLxwIVQ-kUCh38rgL3#v=onepage&q=o%20yu%20schmidt%20problem&f=false  — Preceding unsigned comment added by 193.224.79.1 (talk) 06:27, 28 August 2015 (UTC)
thread_title:  stolen from F. Kennard "Unsolved Problems in Mathematics" p21 

message: I think we should move the "Brief history" section farther down the page, after the "Restricted Burnside problem" section. Right now the history section contains terminology that the reader may not know yet – for example, the exponent of a group is mentioned many times, but not defined until the "Bounded Burnside problem" section. It also mentions periodic groups, while "periodic" isn't defined until the "General Burnside problem" section. Thoughts?
– Pillig (talk) 04:38, 19 May 2019 (UTC)
thread_title:  Move history section 

message: The text asserts, that there were infinite Burnside groups B(m,n) for all integers m>1 and n>8000. The source Лысёнок still has a divisibility condition, i.e. n should be divisible by 16. (see here). Do you have a source for the more general statement in the text?--FerdiBf (talk) 13:06, 4 July 2020 (UTC)
replies: text: According to this review () for any m\ge2 the Burnside group B(m, n) is infinite for odd n \ge 665 (this is indicated to be contained in the book of Adyan) and for n>2^{48} divisible by 2^9 the same holds (by the results of the reviewed article), so Lysënok's result (review here: ) seems to be best available for even exponent (I could not find recent references with a better result). Unless somebody finds a reference with a better result the article should be changed to reflect this jraimbau (talk) 12:44, 7 July 2020 (UTC)
replies: text: just realised that the two results (odd>665 and 16k) together imply the infiniteness of B(2, n) for all integers n >= 16*665=10640. So there is a result for all n large enough. jraimbau (talk) 11:05, 8 July 2020 (UTC)
thread_title:  The bounded problem for large n.