Occurrence problem in a cyclic subgroup in groups with small cancellation conditions C(3)-T(6)

2013 ◽  
Vol 13 (11) ◽  
Author(s):  
Nikolai Bezverhnii
Keyword(s):  
Cyclic Subgroup ◽  
Small Cancellation ◽  
Occurrence Problem

On locally graded barely transitive groups

2013 ◽  
Vol 11 (7) ◽  
Author(s):  
Cansu Betin ◽  
Mahmut Kuzucuoğlu
Keyword(s):  
Finite Index ◽  
Cyclic Subgroup ◽  
Transitive Group ◽  
Transitive Groups ◽  
Point Stabilizer

AbstractWe show that a barely transitive group is totally imprimitive if and only if it is locally graded. Moreover, we obtain the description of a barely transitive group G for the case G has a cyclic subgroup 〈x〉 which intersects non-trivially with all subgroups and for the case a point stabilizer H of G has a subgroup H 1 of finite index in H satisfying the identity χ(H 1) = 1, where χ is a multi-linear commutator of weight w.

scholarly journals Polygonal products of polycyclic by finite groups

1996 ◽  
Vol 54 (3) ◽  
pp. 369-372 ◽  
Author(s):  
R.B.J.T. Allenby
Keyword(s):  
Finite Groups ◽  
Cyclic Subgroup ◽  
Substantial Improvement ◽  
Normal Subgroups ◽  
Recent Theorem

We prove that a polygonal product of polycyclic by finite groups amalgamating normal subgroups, with trivial mutual intersections, is cyclic subgroup separable. Because of a recent example (stated below) of the author this substantial improvement on a recent theorem of Kim is essentially best possible.

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 On the finite $p$-groups with unique cyclic subgroup of given order

2016 ◽  
Vol 40 ◽  
pp. 244-249
Author(s):  
Libo ZHAO ◽  
Yangming LI ◽  
u L\" GONG
Keyword(s):  
Cyclic Subgroup

Powers and conjugacy in small cancellation groups

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

On the Morava K-theory of some finite 2-groups

1997 ◽  
Vol 121 (1) ◽  
pp. 7-13 ◽  
Author(s):  
BJÖRN SCHUSTER
Keyword(s):  
Finite Group ◽  
Sylow Subgroup ◽  
Cyclic Subgroup ◽  
Abelian Groups ◽  
Wreath Products ◽  
Classifying Space ◽  
Generalized Cohomology ◽  
K Theory ◽  
A Finite Group ◽  
Generalized Quaternion

For any fixed prime p and any non-negative integer n there is a 2(pn − 1)-periodic generalized cohomology theory K(n)*, the nth Morava K-theory. Let G be a finite group and BG its classifying space. For some time now it has been conjectured that K(n)*(BG) is concentrated in even dimensions. Standard transfer arguments show that a finite group enjoys this property whenever its p-Sylow subgroup does, so one is reduced to verifying the conjecture for p-groups. It is easy to see that it holds for abelian groups, and it has been proved for some non-abelian groups as well, namely groups of order p3 ([7]) and certain wreath products ([3], [2]). In this note we consider finite (non-abelian) 2-groups with maximal normal cyclic subgroup, i.e. dihedral, semidihedral, quasidihedral and generalized quaternion groups of order a power of two.

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].

Sign in / Sign up

Export Citation Format

Share Document