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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
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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
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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
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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
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In 1964, Golod and
Shafarevich constructed an infinite group of Burnside type without assuming that all elements have uniformly bounded order. In 1968, Pyotr Novikov and Sergei Adian's supplied a negative solution to the bounded exponent problem for all odd exponents larger than
716:) 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
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Defining M to be the intersection of all NORMAL subgroups of finite Index of B(m,n), makes things much easier. See "The
Restricted Burnside Problem" by Michael Vaughan-Lee (available at google books)
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Should the fact that this question has been solved go in the lead of the article? Currently the opening paragraph makes it seem like an open problem.
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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.
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Is there some compelling reason to obfuscate this encyclopedia entry by using the word "order" in one sentence and "exponent" in the next?
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as an author. Paper 1105.0847 is written by Kazuma Morita alone, is in the Number Theory section, and is titled
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In either case, I hope someone knowledgeable on the subject will make this clearer. It certainly needs to be.
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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8000. The source Лысёнок still has a divisibility condition, i.e. n should be divisible by 16. (
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the same holds (by the results of the reviewed article), so Lysënok's result (review here:
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The text asserts, that there were infinite
Burnside groups B(m,n) for all integers m: -->
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The words mean different things. Order here is a property of elements (the order of
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665 and 16k) together imply the infiniteness of B(2, n) for all integers n : -->
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Generalization of the theory of Sen in the semi-stable representation case
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650:(this is indicated to be contained in the book of Adyan) and for
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732:= 16*665=10640. So there is a result for all n large enough.
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stolen from F. Kennard "Unsolved
Problems in Mathematics" p21
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