Finite p-Groups of Nilpotency Class 3 with Two Conjugacy Class Sizes

2017/08/10 by Naik, Tushar Kanta, Kitture, Rahul Dattatraya, Yadav, Manoj K.
#20D15 #20E45 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1708.03245

Abstract

It is proved that, for a prime p>2 and integer n≥ 1, finite p-groups of nilpotency class 3 and having only two conjugacy class sizes 1 and pⁿ exist if and only if n is even; moreover, for a given even positive integer, such a group is unique up to isoclinism (in the sense of Philip Hall).

Related

• Finite p-groups of conjugate type \ 1, p³ \
• A lower bound for the number of conjugacy classes of a finite group
• Finite groups in which almost all class sizes are prime numbers
• Profinite groups with few conjugacy classes of p-elements
• Conjugacy classes and finite p-groups