scholarly journals Generalized small cancellation presentations for automatic groups

2014 ◽  
Vol 0 (0) ◽  
Author(s):  
Robert H. Gilman
Keyword(s):  
Small Cancellation ◽  
Automatic Groups ◽  
Finite Presentations

AbstractBy a result of Gersten and Short finite presentations satisfying the usual non-metric small cancellation conditions present biautomatic groups. We show that in the case in which all pieces have length 1, a generalization of the C(3)-T(6) condition yields a larger collection of biautomatic groups.

Small cancellation theory and automatic groups: Part II

1991 ◽  
Vol 105 (1) ◽  
pp. 641-662 ◽  
Author(s):  
S. M. Gersten ◽  
H. Short
Keyword(s):  
Small Cancellation ◽  
Small Cancellation Theory ◽  
Automatic Groups

Small cancellation theory and automatic groups

1990 ◽  
Vol 102 (1) ◽  
pp. 305-334 ◽  
Author(s):  
S. M. Gersten ◽  
H. B. Short
Keyword(s):  
Small Cancellation ◽  
Small Cancellation Theory ◽  
Automatic Groups

scholarly journals Pro-finite Presentations

2001 ◽  
Vol 242 (2) ◽  
pp. 672-690 ◽  
Author(s):  
Alexander Lubotzky
Keyword(s):  
Finite Presentations

On a conjecture in Artin groups

2021 ◽  
pp. 1-25
Author(s):  
Arye Juhász
Keyword(s):  
Artin Group ◽  
Two Dimensional ◽  
Artin Groups ◽  
Small Cancellation ◽  
Small Cancellation Theory ◽  
Infinite Type ◽  
Trivial Center

It is conjectured that an irreducible Artin group which is of infinite type has trivial center. The conjecture is known to be true for two-dimensional Artin groups and for a few other types of Artin groups. In this work, we show that the conjecture holds true for Artin groups which satisfy a condition stronger than being of infinite type. We use small cancellation theory of relative presentations.

scholarly journals From automatic structures to automatic groups

2014 ◽  
Vol 8 (1) ◽  
pp. 157-198 ◽  
Author(s):  
Olga Kharlampovich ◽  
Bakhadyr Khoussainov ◽  
Alexei Miasnikov
Keyword(s):  
Automatic Structures ◽  
Automatic Groups

Powers and conjugacy in small cancellation groups

1975 ◽  
Vol 26 (1) ◽  
pp. 353-360 ◽  
Author(s):  
Leo P. Comerford
Keyword(s):  
Small Cancellation

scholarly journals A family of two-generator non-Hopfian groups

2017 ◽  
Vol 27 (06) ◽  
pp. 655-675
Author(s):  
Donghi Lee ◽  
Makoto Sakuma
Keyword(s):  
Continued Fraction ◽  
Small Cancellation ◽  
Continued Fraction Expansion ◽  
Link Group

We construct [Formula: see text]-generator non-Hopfian groups [Formula: see text] where each [Formula: see text] has a specific presentation [Formula: see text] which satisfies small cancellation conditions [Formula: see text] and [Formula: see text]. Here, [Formula: see text] is the single relator of the upper presentation of the [Formula: see text]-bridge link group of slope [Formula: see text], where [Formula: see text] and [Formula: see text] in continued fraction expansion for every integer [Formula: see text].

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