The number of subgroups of the group ℤ_m× ℤ_n × ℤ_r × ℤ_s

2016/11/10 by Tóth, László
#11A25 #11Y70 #20K01 #20K27 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1611.03302

Abstract

We deduce direct formulas for the total number of subgroups and the number of subgroups of a given order of the group ℤ_m× ℤ_n × ℤ_r × ℤ_s, where m,n,r,s∈ ℕ. The proofs are by some simple group theoretical and number theoretical arguments based on Goursat's lemma for groups. Two conjectures are also formulated.

Related

• On the number of subgroups of the group ℤ_m₁ × ℤ_m₂ with m₁m₂≤ x such that m₁m₂ is a k-th power
• The distribution of the number of subgroups of the multiplicative group
• An approximation for the number of subgroups
• An explicit upper bound on the number of subgroups of a finite group
• The Number of Subgroups and Cyclic Subgroups of Finite Group and Its Application by GAP Program