Involve: A Journal of Mathematics
- Volume 6, Number 4 (2013), 431-436.
The probability of randomly generating finite abelian groups
Extending the work of Deborah L. Massari and Kimberly L. Patti, this paper makes progress toward finding the probability of elements randomly chosen without repetition generating a finite abelian group, where is the minimum number of elements required to generate the group. A proof of the formula for finding such probabilities of groups of the form , where and is prime, is given, and the result is extended to groups of the form , where and is prime. Examples demonstrating applications of these formulas are given, and aspects of further generalization to finding the probabilities of randomly generating any finite abelian group are investigated.
Involve, Volume 6, Number 4 (2013), 431-436.
Received: 26 July 2012
Revised: 26 October 2012
Accepted: 13 November 2012
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 20P05: Probabilistic methods in group theory [See also 60Bxx]
Carrico, Tyler. The probability of randomly generating finite abelian groups. Involve 6 (2013), no. 4, 431--436. doi:10.2140/involve.2013.6.431. https://projecteuclid.org/euclid.involve/1513733609