ON SUBGROUPS OF A CLASS OF FINITE MINIMAL NONABELIAN 3-GROUP

ON SUBGROUPS OF A CLASS OF FINITE MINIMAL ...

Abstract

In this paper, we determined the number of subgroups of a finite nonabelian 3-group $G $ defined by a presentation
$\rho_{1} \in G = \left\lbrace a,b \mid a^{9} = b^{9} = e, \left[ a,b \right]
= a^{3} \right\rbrace $, where $a, b $ are generators of the same order. The form and the order of elements of the presentation group were obtained. We also drew the diagram of subgroups lattice and derived an explicit formula for counting the number of subgroups of the group.