Examples for Burnside problem.
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What are some examples for Burnside Problem- example of an infinite finitely generated torsion group - except Grigorchuk group.
I have studies Grigorchuk group as an counterexample which was first given to settle this question, but wondering are there other examples. What are they? Any sources to them are welcome.
Thanks
abstract-algebra group-theory combinatorial-group-theory
asked Apr 14 '15 at 19:14
Bhaskar VashishthBhaskar Vashishth
7,61212053
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add a comment |
$begingroup$
What are some examples for Burnside Problem- example of an infinite finitely generated torsion group - except Grigorchuk group.
I have studies Grigorchuk group as an counterexample which was first given to settle this question, but wondering are there other examples. What are they? Any sources to them are welcome.
Thanks
abstract-algebra group-theory combinatorial-group-theory
asked Apr 14 '15 at 19:14
Bhaskar VashishthBhaskar Vashishth
7,61212053
$endgroup$
$begingroup$
There were some examples constructed by Gupta and Sidki, which are similar to the Grigorchuk group, but are based on an odd prime rather than on $2$.
$endgroup$
– Derek Holt
Apr 14 '15 at 20:00
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Tarski Monster group is another example. See en.wikipedia.org/wiki/Tarski_monster_group
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– Crostul
Apr 14 '15 at 20:02
$begingroup$
An example, based on symmetries of a tree, may be found in John Meier's book, Groups, Graphs and Trees. However, the torsion is not uniformely bounded.
$endgroup$
– Seirios
Apr 15 '15 at 5:02
add a comment |
$begingroup$
What are some examples for Burnside Problem- example of an infinite finitely generated torsion group - except Grigorchuk group.
I have studies Grigorchuk group as an counterexample which was first given to settle this question, but wondering are there other examples. What are they? Any sources to them are welcome.
Thanks
abstract-algebra group-theory combinatorial-group-theory
asked Apr 14 '15 at 19:14
Bhaskar VashishthBhaskar Vashishth
7,61212053
$endgroup$
What are some examples for Burnside Problem- example of an infinite finitely generated torsion group - except Grigorchuk group.
I have studies Grigorchuk group as an counterexample which was first given to settle this question, but wondering are there other examples. What are they? Any sources to them are welcome.
Thanks
abstract-algebra group-theory combinatorial-group-theory
abstract-algebra group-theory combinatorial-group-theory
asked Apr 14 '15 at 19:14
Bhaskar VashishthBhaskar Vashishth
7,61212053
asked Apr 14 '15 at 19:14
Bhaskar VashishthBhaskar Vashishth
7,61212053
asked Apr 14 '15 at 19:14
Bhaskar VashishthBhaskar Vashishth
7,61212053
asked Apr 14 '15 at 19:14
Bhaskar VashishthBhaskar Vashishth
7,61212053
asked Apr 14 '15 at 19:14
Bhaskar VashishthBhaskar Vashishth
7,61212053
7,61212053
$begingroup$
There were some examples constructed by Gupta and Sidki, which are similar to the Grigorchuk group, but are based on an odd prime rather than on $2$.
$endgroup$
– Derek Holt
Apr 14 '15 at 20:00
$begingroup$
Tarski Monster group is another example. See en.wikipedia.org/wiki/Tarski_monster_group
$endgroup$
– Crostul
Apr 14 '15 at 20:02
$begingroup$
An example, based on symmetries of a tree, may be found in John Meier's book, Groups, Graphs and Trees. However, the torsion is not uniformely bounded.
$endgroup$
– Seirios
Apr 15 '15 at 5:02
add a comment |
$begingroup$
There were some examples constructed by Gupta and Sidki, which are similar to the Grigorchuk group, but are based on an odd prime rather than on $2$.
$endgroup$
– Derek Holt
Apr 14 '15 at 20:00
$begingroup$
Tarski Monster group is another example. See en.wikipedia.org/wiki/Tarski_monster_group
$endgroup$
– Crostul
Apr 14 '15 at 20:02
$begingroup$
An example, based on symmetries of a tree, may be found in John Meier's book, Groups, Graphs and Trees. However, the torsion is not uniformely bounded.
$endgroup$
– Seirios
Apr 15 '15 at 5:02
$begingroup$
There were some examples constructed by Gupta and Sidki, which are similar to the Grigorchuk group, but are based on an odd prime rather than on $2$.
$endgroup$
– Derek Holt
Apr 14 '15 at 20:00
$begingroup$
There were some examples constructed by Gupta and Sidki, which are similar to the Grigorchuk group, but are based on an odd prime rather than on $2$.
$endgroup$
– Derek Holt
Apr 14 '15 at 20:00
$begingroup$
Tarski Monster group is another example. See en.wikipedia.org/wiki/Tarski_monster_group
$endgroup$
– Crostul
Apr 14 '15 at 20:02
$begingroup$
Tarski Monster group is another example. See en.wikipedia.org/wiki/Tarski_monster_group
$endgroup$
– Crostul
Apr 14 '15 at 20:02
$begingroup$
An example, based on symmetries of a tree, may be found in John Meier's book, Groups, Graphs and Trees. However, the torsion is not uniformely bounded.
$endgroup$
– Seirios
Apr 15 '15 at 5:02
$begingroup$
An example, based on symmetries of a tree, may be found in John Meier's book, Groups, Graphs and Trees. However, the torsion is not uniformely bounded.
$endgroup$
– Seirios
Apr 15 '15 at 5:02
add a comment |
1 Answer
1
active
oldest
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Show me a infinite finitely generated group that is not also infinitely generated and I'll believe that there is a counterexample for the Burnside problem. E.g.,
$mathbb{Z}=,<{1}>$ but also $mathbb{Z}=,<{p,,|,,p,,mathrm{is,prime}}>$ .
answered Nov 28 '18 at 5:54
Andrew NavaAndrew Nava
11
$endgroup$
$begingroup$
You missed the word 'torsion' here.
$endgroup$
– Bhaskar Vashishth
Nov 30 '18 at 18:35
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Show me a infinite finitely generated group that is not also infinitely generated and I'll believe that there is a counterexample for the Burnside problem. E.g.,
$mathbb{Z}=,<{1}>$ but also $mathbb{Z}=,<{p,,|,,p,,mathrm{is,prime}}>$ .
answered Nov 28 '18 at 5:54
Andrew NavaAndrew Nava
11
$endgroup$
$begingroup$
You missed the word 'torsion' here.
$endgroup$
– Bhaskar Vashishth
Nov 30 '18 at 18:35
add a comment |
$begingroup$
Show me a infinite finitely generated group that is not also infinitely generated and I'll believe that there is a counterexample for the Burnside problem. E.g.,
$mathbb{Z}=,<{1}>$ but also $mathbb{Z}=,<{p,,|,,p,,mathrm{is,prime}}>$ .
answered Nov 28 '18 at 5:54
Andrew NavaAndrew Nava
11
$endgroup$
$begingroup$
You missed the word 'torsion' here.
$endgroup$
– Bhaskar Vashishth
Nov 30 '18 at 18:35
add a comment |
$begingroup$
Show me a infinite finitely generated group that is not also infinitely generated and I'll believe that there is a counterexample for the Burnside problem. E.g.,
$mathbb{Z}=,<{1}>$ but also $mathbb{Z}=,<{p,,|,,p,,mathrm{is,prime}}>$ .
answered Nov 28 '18 at 5:54
Andrew NavaAndrew Nava
11
$endgroup$
Show me a infinite finitely generated group that is not also infinitely generated and I'll believe that there is a counterexample for the Burnside problem. E.g.,
$mathbb{Z}=,<{1}>$ but also $mathbb{Z}=,<{p,,|,,p,,mathrm{is,prime}}>$ .
answered Nov 28 '18 at 5:54
Andrew NavaAndrew Nava
11
answered Nov 28 '18 at 5:54
Andrew NavaAndrew Nava
11
answered Nov 28 '18 at 5:54
Andrew NavaAndrew Nava
11
answered Nov 28 '18 at 5:54
Andrew NavaAndrew Nava
11
11
$begingroup$
You missed the word 'torsion' here.
$endgroup$
– Bhaskar Vashishth
Nov 30 '18 at 18:35
add a comment |
$begingroup$
You missed the word 'torsion' here.
$endgroup$
– Bhaskar Vashishth
Nov 30 '18 at 18:35
$begingroup$
You missed the word 'torsion' here.
$endgroup$
– Bhaskar Vashishth
Nov 30 '18 at 18:35
$begingroup$
You missed the word 'torsion' here.
$endgroup$
– Bhaskar Vashishth
Nov 30 '18 at 18:35
add a comment |
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$begingroup$
There were some examples constructed by Gupta and Sidki, which are similar to the Grigorchuk group, but are based on an odd prime rather than on $2$.
$endgroup$
– Derek Holt
Apr 14 '15 at 20:00
$begingroup$
Tarski Monster group is another example. See en.wikipedia.org/wiki/Tarski_monster_group
$endgroup$
– Crostul
Apr 14 '15 at 20:02
$begingroup$
An example, based on symmetries of a tree, may be found in John Meier's book, Groups, Graphs and Trees. However, the torsion is not uniformely bounded.
$endgroup$
– Seirios
Apr 15 '15 at 5:02