All Questions
Tagged with combinatorial-group-theory reference-request
18 questions
3
votes
1
answer
165
views
When the fundamental group of subgraph of groups embeds?
Given a connected graph of groups $\mathcal G$ (where edge maps are embeddings), by a subgraph we mean a graph of groups obtain by omitting some vertices, some edges, and replacing the remaining ...
- 1,338
1
vote
0
answers
75
views
Cohomological finiteness (boundedness) property
Let $G$ be arbitrary group. Let us assume it is $\operatorname{FP}_\infty$. Suppose that the integral cohomology groups $H^i(G, \mathbb{Z})$ have bounded rank as finitely generated free abelian groups ...
- 383
17
votes
3
answers
1k
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Examples of locally hyperbolic groups
It is well-known that a subgroup of a hyperbolic group need not be hyperbolic. Let us say that a (finitely generated) group $G$ is locally hyperbolic if all its finitely generated subgroups are (...
- 383
1
vote
1
answer
259
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Which properties can be read off the balls of a Cayley graph?
For which properties (P) [of groups] does the following hold:
given a group $G$ which has a finite presentation with at most $n$ relations of length at most $\ell$, there is a $R(n,\ell)$ so that, if ...
- 4,432
8
votes
0
answers
125
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The conjugacy problem for two-relator groups
Is the conjugacy problem for two-relator groups known to be undecidable?
The word problem for two-relator groups is a famous open problem (appearing e.g. as Question 9.29 in the Kourovka notebook), ...
10
votes
2
answers
410
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Reference request: Recent progress on the conjugacy problem for torsion-free one-relator groups?
I am aware that the Spelling Theorem of B. B. Newman implies that one-relator groups with torsion are hyperbolic, and thus have a solvable conjugacy problem. My understanding is that for one-relator ...
- 629
2
votes
0
answers
137
views
Time complexity of randomized algorithm: right-multiplying by random elements $z_i$ from a group $H$ to achieve $H$-invariance
Note: This question was inspired by a related question about the Quantum Merlin Arthur (QMA) complexity class on Quantum Computing Stack Exchange. I was deliberating whether to ask this on CS Theory ...
- 269
4
votes
3
answers
282
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Conjugacy in right-angled Artin groups
I am looking for a reference containing the following result:
Let $a$ and $b$ be two elements of a right-angled Artin group $A$. Assume that $a$ and $b$ have minimal length (with respect to the ...
- 8,401
13
votes
1
answer
1k
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Is there a name of semidirect product of a group with its automorphism group?
Consider the construction $G \rtimes \text{Aut}(G)$. Here $
G$ is a group, $\text{Aut}(G)$ is the automorphism group and the semidirect product is over the most obvious action.
1) Is there any name ...
- 885
11
votes
0
answers
379
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Amalgamated product of automatic groups
In Gersten's "Problems on Automatic Groups", Problem 14, he asks the following question: Let $G=A\ast_{C}B$ where $A$ and $B$ are automatic and $C$ is infinite cyclic. Is $G$ automatic?
Is this ...
- 525
2
votes
1
answer
439
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Quotient groups of the lower central series of a surface group
In the answer to MO question 132247, it is possible to find a nice computation of the quotient groups of the lower central series of a finitely generated free group.
Q. What are the quotient ...
- 66.3k
6
votes
1
answer
441
views
Minimum number of operations necessary to arrive at any configuration
Let $k \geq 2$ and $N_1, N_2, ..., N_k$ be positive integers.
Let $S=\{(a_1,a_2,...,a_k) \in \mathbb{Z}^k:1 \leq a_i \leq N_i\}$ and $A=\{1,2,...,\prod_{i=1}^{k} N_{i}\}$.
Given a bijective map $f:...
- 3,153
6
votes
1
answer
405
views
An algorithm determining whether two subgroups of a finitely generated free group are automorphic
In the book Lyndon, Schupp, Combinatorial Group Theory, P.30 in the edition from 2000 They mention an unpublished work by Waldhausen that is said to give an algorithm to determine whether two ...
- 193
3
votes
1
answer
306
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Reference request for non-commutative analogues of exterior algebras
I am reading Combinatorial Group Theory In Homotopy Theory I by Fred Cohen (preprint available on web page). Here is an extract of the paper:
Cohen called $A^R_n$ "a standard tool used in ...
- 1,108
10
votes
2
answers
815
views
Paper by I. N. Sanov, Solution of the Burnside problem for exponent 4
I have searched extensively online and for copies of printed journals containing the paper which details Sanov's solution to the Burnside Problem for exponent 4, which is widely cited in many papers ...
- 201
1
vote
1
answer
178
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Request a paper by Fred Cohen
I am looking for the following paper by Cohen, F. R.:
On combinatorial group theory in homotopy. Homotopy theory and its
applications (Cocoyoc, 1993), 57–63, Contemp. Math., 188, Amer. Math.
...
- 1,108
13
votes
3
answers
2k
views
Which groups are LERF?
A finitely generated group $G$ is called LERF if every finitely generated $H \leq G$ is closed in the profinite topology on $G$ (equivalently, there is a family of finite index subgroups of $G$ ...
- 11.3k
17
votes
1
answer
2k
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A synopsis of Adyan’s solution to the general Burnside problem?
Where can I find a high-level overview
of Adyan’s original proof of the existence of finitely generated infinite groups with finite exponent?
Additionally:
If possible, would an expert please ...
- 7,057