The Number of Subgroups and Cyclic Subgroups of Finite Group and Its Application by GAP Program
Abstract
In this work, In this paper, we presented A novel approach for calculating a finite group's set of subgroups, cyclic subgroups using it to establish the quantity of all subgroups in the direct product of two groups, the Dicyclic group have order and the Cyclic group have order , is a total number of all divisors of and the summation of all divisors, . Using this, we derive a formula for the number of subgroups in the group . We then use the computer program GAP to find all with exactly | | − t cyclic subgroups for .
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