Translator Disclaimer
2013 The probability of randomly generating finite abelian groups
Tyler Carrico
Involve 6(4): 431-436 (2013). DOI: 10.2140/involve.2013.6.431

Abstract

Extending the work of Deborah L. Massari and Kimberly L. Patti, this paper makes progress toward finding the probability of k elements randomly chosen without repetition generating a finite abelian group, where k 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 pmpn, where m,n and p is prime, is given, and the result is extended to groups of the form pn1pnk, where ni,k and p 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.

Citation

Download Citation

Tyler Carrico. "The probability of randomly generating finite abelian groups." Involve 6 (4) 431 - 436, 2013. https://doi.org/10.2140/involve.2013.6.431

Information

Received: 26 July 2012; Revised: 26 October 2012; Accepted: 13 November 2012; Published: 2013
First available in Project Euclid: 20 December 2017

zbMATH: 1280.20069
MathSciNet: MR3115976
Digital Object Identifier: 10.2140/involve.2013.6.431

Subjects:
Primary: 20P05

Rights: Copyright © 2013 Mathematical Sciences Publishers

JOURNAL ARTICLE
6 PAGES


SHARE
Vol.6 • No. 4 • 2013
MSP
Back to Top