#### Title

#### Document Type

Article

#### Publication Date

9-1992

#### First Advisor

Gary Sherman

#### Abstract

In this paper , we consider the probability that two elements chosen at random from a finite group G generate a subgroup of a given nilpotency class. It is shown that in solvable non-nilpotent groups, the probability that two elements generate a nilpotent subgroup is <= *l/p*,, where *p, *is the smallest prime dividing the order of the group, and it is also shown that there exist groups such that the probability of two elements generating a subgroup of class i approaches one (and other groups for which it approaches zero) for all* i =>2.* It is also shown that the number of pairs which generate a subgroup of a given class is always a multiple of the order of the group. Some preliminary results on the analogous problem for solvability are also given.

#### Recommended Citation

Fulman, Jason; Galloy, Michael; and Vanderkam, Jeffery, "Counting Nilpotent Pairs" (1992). *Mathematical Sciences Technical Reports (MSTR)*. 135.

https://scholar.rose-hulman.edu/math_mstr/135

## Comments

MSTR 92-08