DEFICIENCY ZERO GROUPS IN WHICH PRIME POWER OF GENERATORS ARE CENTRAL
نویسندگان
1 Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, P.O.Box 56199-11367, Ardabil, Iran.
2 Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, P.O.Box 56199-11367, Ardabil, Iran.
doi
10.22044/jas.2020.9361.1456چکیده
The infinite family of groups defined by the presentation $G_p=\langle x, y|x^p=y^p,\; xyx^my^n=1\rangle$, in which $p$ is a prime in $\{2,3,5\}$ and $m,n\in\mathbb{N}_0$, will be considered and finite and infinite groups in the family will be determined. For the primes $p=2,3$ the group $G_p$ is finite and for $p=5$, the group is finite if and only if $m\equiv n\equiv1\pmod5$ is not the case.
