Conjugacy separability of certain HNN extensions with normal associated subgroups
Kok Bin
Wong
University of Malaya
author
Peng Choon
Wong
University of Malaya
author
text
article
2016
eng
In this paper, we will give necessary and sufficient conditions for certain HNN extensions of subgroup separable groups with normal associated subgroup to be conjugacy separable. In fact, we will show that these HNN extensions are conjugacy separable if and only if the normalizer of one of its associated subgroup is conjugacy separable..
International Journal of Group Theory
University of Isfahan
2251-7650
5
v.
4
no.
2016
1
16
http://ijgt.ui.ac.ir/article_9021_5b20379e91df928a3137f1607a1fb81c.pdf
dx.doi.org/10.22108/ijgt.2016.9021
A note on the coprime graph of a group
Hamid Reza
Dorbidi
Department of Basic Sciences, University of Jiroft, Jiroft, Kerman, Iran
author
text
article
2016
eng
In this paper we study the coprime graph of a group $G$. The coprime graph of a group $G$, denoted by $\Gamma_G$, is a graph whose vertices are elements of $G$ and two distinct vertices $x$ and $y$ are adjacent if and only if $(|x|,|y|)=1$. In this paper, we show that $\chi(\Gamma_G)=\omega(\Gamma_G).$ We classify all the groups which $\Gamma_G$ is a complete $r-$partite graph or a planar graph. Also we study the automorphism group of $\Gamma_G$.
International Journal of Group Theory
University of Isfahan
2251-7650
5
v.
4
no.
2016
17
22
http://ijgt.ui.ac.ir/article_9125_60914131d24633f1c40065d684308824.pdf
dx.doi.org/10.22108/ijgt.2016.9125
A remark on group rings of periodic groups
Artur
Grigoryan
Assitant at Armenian-Russian State University
author
text
article
2016
eng
A positive solution of the problem of the existence of nontrivial pairs of zero-divisors in group rings of free Burnside groups of sufficiently large odd periods $n>10^{10}$ obtained previously by S. V. Ivanov and R. Mikhailov extended to all odd periods $n\geq665$.
International Journal of Group Theory
University of Isfahan
2251-7650
5
v.
4
no.
2016
23
25
http://ijgt.ui.ac.ir/article_9425_720ff6144bb244550dc6257a3e3a9ebc.pdf
dx.doi.org/10.22108/ijgt.2016.9425
A gap theorem for the ZL-amenability constant of a finite group
Yemon
Choi
Lancaster University
author
text
article
2016
eng
It was shown in [A. Azimifard, E. Samei and N. Spronk, Amenability properties of the centres of group algebras, J. Funct. Anal., 256 no. 5 (2009) 1544-1564.] that the ZL-amenability constant of a finite group is always at least $1$, with equality if and only if the group is abelian. It was also shown that for any finite non-abelian group this invariant is at least $301/300$, but the proof relies crucially on a deep result of D. A. Rider on norms of central idempotents in group algebras. Here we show that if $G$ is finite and non-abelian then its ZL-amenability constant is at least $7/4$, which is known to be best possible. We avoid use of Rider's reslt, by analyzing the cases where $G$ is just non-abelian, using calculations from [M. Alaghmandan, Y. Choi and E. Samei, ZL-amenability constants of finite groups with two character degrees, Canad. Math. Bull., 57 (2014) 449-462.], and establishing a new estimate for groups with trivial centre.
International Journal of Group Theory
University of Isfahan
2251-7650
5
v.
4
no.
2016
27
46
http://ijgt.ui.ac.ir/article_9562_6ce2f0b168ba2560656bbdd6cd54eaae.pdf
dx.doi.org/10.22108/ijgt.2016.9562
A note on transfer theorems
Haoran
Yu
Peking University
author
text
article
2016
eng
In this paper, we generalize some transfer theorems. In particular, we derive one of the main results of Gagola (Contemp Math., 524 (2010) 49-60) from our results.
International Journal of Group Theory
University of Isfahan
2251-7650
5
v.
4
no.
2016
47
52
http://ijgt.ui.ac.ir/article_9851_dbe5354f39be697773b5bfa97d171fec.pdf
dx.doi.org/10.22108/ijgt.2016.9851