Mixing
Kropholler's Type of Tits Alternative for Generalised Baumslag-Solitar Groups.
up vote
2
down vote
favorite
In "Recent Results on Generalized
Baumslag-Solitar Groups," by D.J.S Robinson in Note Mat. 30 (2010) suppl. n. 1, 37–53, it is claimed that
Kropholler [ . . . ] showed that there is a type of Tits alternative for GBS-groups, (Kropholler [11]).
[11] Baumslag-Solitar groups and some other groups of cohomological dimension two
The problem is that I need to know what type of Tits alternative holds for GBS-groups but, unfortunately, I can't get a hold of the relevant paper. It's behind a pay wall and my local university library isn't subscribed to the journal.
Please would someone clarify the type of Tits alternative for the GBS-groups for me here?
:)
group-theory graph-theory combinatorial-group-theory
edited yesterday
Paul Plummer
4,78921950
asked yesterday
Shaun
7,787113277
add a comment |
up vote
2
down vote
favorite
In "Recent Results on Generalized
Baumslag-Solitar Groups," by D.J.S Robinson in Note Mat. 30 (2010) suppl. n. 1, 37–53, it is claimed that
Kropholler [ . . . ] showed that there is a type of Tits alternative for GBS-groups, (Kropholler [11]).
[11] Baumslag-Solitar groups and some other groups of cohomological dimension two
The problem is that I need to know what type of Tits alternative holds for GBS-groups but, unfortunately, I can't get a hold of the relevant paper. It's behind a pay wall and my local university library isn't subscribed to the journal.
Please would someone clarify the type of Tits alternative for the GBS-groups for me here?
:)
group-theory graph-theory combinatorial-group-theory
edited yesterday
Paul Plummer
4,78921950
asked yesterday
Shaun
7,787113277
add a comment |
up vote
2
down vote
favorite
up vote
2
down vote
favorite
In "Recent Results on Generalized
Baumslag-Solitar Groups," by D.J.S Robinson in Note Mat. 30 (2010) suppl. n. 1, 37–53, it is claimed that
Kropholler [ . . . ] showed that there is a type of Tits alternative for GBS-groups, (Kropholler [11]).
[11] Baumslag-Solitar groups and some other groups of cohomological dimension two
The problem is that I need to know what type of Tits alternative holds for GBS-groups but, unfortunately, I can't get a hold of the relevant paper. It's behind a pay wall and my local university library isn't subscribed to the journal.
Please would someone clarify the type of Tits alternative for the GBS-groups for me here?
:)
group-theory graph-theory combinatorial-group-theory
edited yesterday
Paul Plummer
4,78921950
asked yesterday
Shaun
7,787113277
In "Recent Results on Generalized
Baumslag-Solitar Groups," by D.J.S Robinson in Note Mat. 30 (2010) suppl. n. 1, 37–53, it is claimed that
Kropholler [ . . . ] showed that there is a type of Tits alternative for GBS-groups, (Kropholler [11]).
[11] Baumslag-Solitar groups and some other groups of cohomological dimension two
The problem is that I need to know what type of Tits alternative holds for GBS-groups but, unfortunately, I can't get a hold of the relevant paper. It's behind a pay wall and my local university library isn't subscribed to the journal.
Please would someone clarify the type of Tits alternative for the GBS-groups for me here?
:)
group-theory graph-theory combinatorial-group-theory
group-theory graph-theory combinatorial-group-theory
edited yesterday
Paul Plummer
4,78921950
asked yesterday
Shaun
7,787113277
edited yesterday
Paul Plummer
4,78921950
asked yesterday
Shaun
7,787113277
edited yesterday
Paul Plummer
4,78921950
edited yesterday
Paul Plummer
4,78921950
edited yesterday
Paul Plummer
4,78921950
4,78921950
asked yesterday
Shaun
7,787113277
asked yesterday
Shaun
7,787113277
asked yesterday
Shaun
7,787113277
7,787113277
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
up vote
4
down vote
accepted
Recent results on generalized Baumslag-Solitar groups does describe what they mean (maybe in a somewhat round about way).
The type of Tits alternative is this: Finitely generated subgroups of GBS-groups are either solvable or contain non-abelian free subgroups.
The above statement follows from the theorems they mention:
Theorem 1: The second derived subgroup of a GBS-group is free.
In particular GBS-groups are solvable exactly when the second derived subgroup is trivial or $mathbb Z$. Otherwise it contains a higher rank free subgroup, so can not be solvable.
Theorem 2: Finitely generated subgroups of GBS-group are either free or GBS-groups.
This theorem gives us a way to apply theorem 1 to finitely generated subgroups of GBS-groups. This finishes the proof of "finitely generated Tits alternative".
answered yesterday
Paul Plummer
4,78921950
Well spotted. Thank you :)
– Shaun
yesterday
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
4
down vote
accepted
Recent results on generalized Baumslag-Solitar groups does describe what they mean (maybe in a somewhat round about way).
The type of Tits alternative is this: Finitely generated subgroups of GBS-groups are either solvable or contain non-abelian free subgroups.
The above statement follows from the theorems they mention:
Theorem 1: The second derived subgroup of a GBS-group is free.
In particular GBS-groups are solvable exactly when the second derived subgroup is trivial or $mathbb Z$. Otherwise it contains a higher rank free subgroup, so can not be solvable.
Theorem 2: Finitely generated subgroups of GBS-group are either free or GBS-groups.
This theorem gives us a way to apply theorem 1 to finitely generated subgroups of GBS-groups. This finishes the proof of "finitely generated Tits alternative".
answered yesterday
Paul Plummer
4,78921950
Well spotted. Thank you :)
– Shaun
yesterday
add a comment |
up vote
4
down vote
accepted
Recent results on generalized Baumslag-Solitar groups does describe what they mean (maybe in a somewhat round about way).
The type of Tits alternative is this: Finitely generated subgroups of GBS-groups are either solvable or contain non-abelian free subgroups.
The above statement follows from the theorems they mention:
Theorem 1: The second derived subgroup of a GBS-group is free.
In particular GBS-groups are solvable exactly when the second derived subgroup is trivial or $mathbb Z$. Otherwise it contains a higher rank free subgroup, so can not be solvable.
Theorem 2: Finitely generated subgroups of GBS-group are either free or GBS-groups.
This theorem gives us a way to apply theorem 1 to finitely generated subgroups of GBS-groups. This finishes the proof of "finitely generated Tits alternative".
answered yesterday
Paul Plummer
4,78921950
Well spotted. Thank you :)
– Shaun
yesterday
add a comment |
up vote
4
down vote
accepted
up vote
4
down vote
accepted
Recent results on generalized Baumslag-Solitar groups does describe what they mean (maybe in a somewhat round about way).
The type of Tits alternative is this: Finitely generated subgroups of GBS-groups are either solvable or contain non-abelian free subgroups.
The above statement follows from the theorems they mention:
Theorem 1: The second derived subgroup of a GBS-group is free.
In particular GBS-groups are solvable exactly when the second derived subgroup is trivial or $mathbb Z$. Otherwise it contains a higher rank free subgroup, so can not be solvable.
Theorem 2: Finitely generated subgroups of GBS-group are either free or GBS-groups.
This theorem gives us a way to apply theorem 1 to finitely generated subgroups of GBS-groups. This finishes the proof of "finitely generated Tits alternative".
answered yesterday
Paul Plummer
4,78921950
Recent results on generalized Baumslag-Solitar groups does describe what they mean (maybe in a somewhat round about way).
The type of Tits alternative is this: Finitely generated subgroups of GBS-groups are either solvable or contain non-abelian free subgroups.
The above statement follows from the theorems they mention:
Theorem 1: The second derived subgroup of a GBS-group is free.
In particular GBS-groups are solvable exactly when the second derived subgroup is trivial or $mathbb Z$. Otherwise it contains a higher rank free subgroup, so can not be solvable.
Theorem 2: Finitely generated subgroups of GBS-group are either free or GBS-groups.
This theorem gives us a way to apply theorem 1 to finitely generated subgroups of GBS-groups. This finishes the proof of "finitely generated Tits alternative".
answered yesterday
Paul Plummer
4,78921950
edited yesterday
answered yesterday
Paul Plummer
4,78921950
answered yesterday
Paul Plummer
4,78921950
answered yesterday
Paul Plummer
4,78921950
4,78921950
Well spotted. Thank you :)
– Shaun
yesterday
add a comment |
Well spotted. Thank you :)
– Shaun
yesterday
Well spotted. Thank you :)
– Shaun
yesterday
Well spotted. Thank you :)
– Shaun
yesterday
add a comment |
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3005194%2fkrophollers-type-of-tits-alternative-for-generalised-baumslag-solitar-groups%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
