scholarly journals On a small cancellation theorem of Gromov

2006 ◽  
Vol 13 (1) ◽  
pp. 75-89 ◽  
Author(s):  
Yann Ollivier
Keyword(s):  
Small Cancellation ◽  
Cancellation Theorem

scholarly journals Introduction to a small cancellation theorem

2021 ◽  
Vol 13 (1) ◽  
pp. 79-102
Author(s):  
Stéphane Lamy ◽  
Anne Lonjou
Keyword(s):  
Small Cancellation ◽  
Cancellation Theorem

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.

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].

scholarly journals Cogrowth for group actions with strongly contracting elements

2018 ◽  
Vol 40 (7) ◽  
pp. 1738-1754 ◽  
Author(s):  
GOULNARA N. ARZHANTSEVA ◽  
CHRISTOPHER H. CASHEN
Keyword(s):  
Mapping Class Groups ◽  
Hyperbolic Spaces ◽  
Hyperbolic Groups ◽  
Mapping Class ◽  
Small Cancellation ◽  
Class Groups ◽  
Original Result ◽  
Geodesic Metric Space ◽  
Geodesic Metric ◽  
Right Angled Artin Groups

Let $G$ be a group acting properly by isometries and with a strongly contracting element on a geodesic metric space. Let $N$ be an infinite normal subgroup of $G$ and let $\unicode[STIX]{x1D6FF}_{N}$ and $\unicode[STIX]{x1D6FF}_{G}$ be the growth rates of $N$ and $G$ with respect to the pseudo-metric induced by the action. We prove that if $G$ has purely exponential growth with respect to the pseudo-metric, then $\unicode[STIX]{x1D6FF}_{N}/\unicode[STIX]{x1D6FF}_{G}>1/2$. Our result applies to suitable actions of hyperbolic groups, right-angled Artin groups and other CAT(0) groups, mapping class groups, snowflake groups, small cancellation groups, etc. This extends Grigorchuk’s original result on free groups with respect to a word metric and a recent result of Matsuzaki, Yabuki and Jaerisch on groups acting on hyperbolic spaces to a much wider class of groups acting on spaces that are not necessarily hyperbolic.

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