# Journal of the Ramanujan Mathematical Society

Volume 38, Issue 3, September 2023 pp. 275–293.

Simultaneous Conjugacy Classes of Finite p-groups of rank ≤ 5

**Authors**:
Dilpreet Kaur, Sunil Kumar Prajapati and Amritanshu Prasad

**Author institution:**
Indian Institute of Technology Jodhpur, NH 65, Surpura Bypass Rd, Karwar, Rajasthan 342 037, India.

**Summary: **
For a finite group G, we consider the problem of counting simultaneous
conjugacy classes of n-tuples and simultaneous conjugacy classes of commuting
n-tuples in G. Let α{G,n} denote the number of simultaneous conjugacy
classes of n-tuples, and β{G,n} the number of simultaneous conjugacy
classes of commuting n-tuples in G. The generating functions A{G}(t) = Σ
{n ≥ 0} α{G,n} t{n}, and B{G}(t) = Σ{n ≥ 0} β{G,n}
t{n} are rational functions of t. In this paper we study normalized functions
A{G}(t/|G|) and B{G}(t/|G|) for finite p-groups of rank at most 5.

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