University of Isfahan International Journal of Group Theory 2251-7650 6 3 2017 09 01 Finite $2$-groups of class $2$ with a specific automorphism group 1 4 20362 10.22108/ijgt.2017.20362 EN Marzieh Ahmadi University of Isfahan S. Mohsen Ghoraishi Shahid Chamran university of Ahvaz Journal Article 2016 04 26 ‎‎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. ‎‎Finite $p$-group of class $2$‎ ‎non-inner automorphism‎ ‎Frattini subgroup https://ijgt.ui.ac.ir/article_20362_2ad6e4d061e43064bb40cf6fd363382b.pdf
University of Isfahan International Journal of Group Theory 2251-7650 6 3 2017 09 01 An extension and a generalization of Dedekind's theorem 5 11 21238 10.22108/ijgt.2017.21238 EN Naoya Yamaguchi Kyushu University Journal Article 2016 07 12 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. ‎Dedekind's theorem group determinant group algebra https://ijgt.ui.ac.ir/article_21238_0fd33ba67df03d3f2b788744321dba1e.pdf
University of Isfahan International Journal of Group Theory 2251-7650 6 3 2017 09 01 One-prime power hypothesis for conjugacy class sizes 13 19 12043 10.22108/ijgt.2017.12043 EN Alan Camina University of East Anglia Rachel Camina Fitzwilliam College, University of Cambridge Journal Article 2015 11 02 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. conjugacy class sizes Finite groups insoluble groups bipartite graph https://ijgt.ui.ac.ir/article_12043_81116a607ca09117e53c05589eda4c89.pdf
University of Isfahan International Journal of Group Theory 2251-7650 6 3 2017 09 01 Right amenable left group sets and the Tarski-Følner theorem 21 44 21243 10.22108/ijgt.2017.21243 EN Simon Wacker Karlsruhe Institute of Technology Journal Article 2016 08 16 ‎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. ‎‎left group actions‎ ‎right amenability‎ ‎right FØlner nets‎ ‎right paradoxical decompositions‎ ‎Tarski-FØlner theorem https://ijgt.ui.ac.ir/article_21243_e2bcc02dd5065368c194914a01d42fd1.pdf
University of Isfahan International Journal of Group Theory 2251-7650 6 3 2017 09 01 An infinite family of finite ‎$‎2‎$‎-groups with deficiency zero 45 49 21213 10.22108/ijgt.2017.21213 EN Hossein Abdolzadeh University of Mohaghegh Ardabili Reza Sabzchi University of Mohaghegh Ardabili Journal Article 2016 12 06 ‎‎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. ‎finite $2$-groups‎ ‎deficiency zero‎ ‎Schur multiplicator https://ijgt.ui.ac.ir/article_21213_a382f42475f8370fbd5fbd0c172cc39c.pdf