Finite $2$-groups of class $2$ with a specific automorphism group
S. Mohsen
Ghoraishi
Shahid Chamran university of Ahvaz
author
Marzieh
Ahmadi
University of Isfahan
author
text
article
2017
eng
In this paper we determine all finite $2$-groups of class $2$ in which every automorphism of order $2$ leaving the Frattini subgroup elementwise fixed is inner.
International Journal of Group Theory
University of Isfahan
2251-7650
6
v.
3
no.
2017
1
4
http://ijgt.ui.ac.ir/article_20362_2ad6e4d061e43064bb40cf6fd363382b.pdf
dx.doi.org/10.22108/ijgt.2017.20362
An extension and a generalization of Dedekind's theorem
Naoya
Yamaguchi
Kyushu University
author
text
article
2017
eng
For any given finite abelian group, we give factorizations of the group determinant in the group algebra of any subgroups. The factorizations is an extension of Dedekind's theorem. The extension leads to a generalization of Dedekind's theorem.
International Journal of Group Theory
University of Isfahan
2251-7650
6
v.
3
no.
2017
5
11
http://ijgt.ui.ac.ir/article_21238_0fd33ba67df03d3f2b788744321dba1e.pdf
dx.doi.org/10.22108/ijgt.2017.21238
One-prime power hypothesis for conjugacy class sizes
Alan
Camina
University of East Anglia
author
Rachel
Camina
Fitzwilliam College, University of Cambridge
author
text
article
2017
eng
A finite group $G$ satisfies the on-prime power hypothesis for conjugacy class sizes if any two conjugacy class sizes $m$ and $n$ are either equal or have a common divisor a prime power. Taeri conjectured that an insoluble group satisfying this condition is isomorphic to $S times A$ where $A$ is abelian and $S cong PSL_2(q)$ for $q in {4,8}$. We confirm this conjecture.
International Journal of Group Theory
University of Isfahan
2251-7650
6
v.
3
no.
2017
13
19
http://ijgt.ui.ac.ir/article_12043_81116a607ca09117e53c05589eda4c89.pdf
dx.doi.org/10.22108/ijgt.2017.12043
Right amenable left group sets and the Tarski-FØlner theorem
Simon
Wacker
Karlsruhe Institute of Technology
author
text
article
2017
eng
We introduce right amenability, right FØlner nets, and right paradoxical decompositions for left homogeneous spaces and prove the Tarski-FØlner theorem for left homogeneous spaces with finite stabilisers. It states that right amenability, the existence of right FØlner nets, and the non-existence of right paradoxical decompositions are equivalent.
International Journal of Group Theory
University of Isfahan
2251-7650
6
v.
3
no.
2017
21
44
http://ijgt.ui.ac.ir/article_21243_e2bcc02dd5065368c194914a01d42fd1.pdf
dx.doi.org/10.22108/ijgt.2017.21243
An infinite family of finite $2$-groups with deficiency zero
Hossein
Abdolzadeh
University of Mohaghegh Ardabili
author
Reza
Sabzchi
University of Mohaghegh Ardabili
author
text
article
2017
eng
We determine a new infinite sequence of finite $2$-groups with deficiency zero. The groups have $2$ generators and $2$ relations, they have coclass $3$ and they are not metacyclic.
International Journal of Group Theory
University of Isfahan
2251-7650
6
v.
3
no.
2017
45
49
http://ijgt.ui.ac.ir/article_21213_625c1b20ac51e2b4be1b5623bb829991.pdf
dx.doi.org/10.22108/ijgt.2017.21213