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


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.


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Tyler Carrico. "The probability of randomly generating finite abelian groups." Involve 6 (4) 431 - 436, 2013.


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

Primary: 20P05

Keywords: abelian , generate , group , Probability

Rights: Copyright © 2013 Mathematical Sciences Publishers


Vol.6 • No. 4 • 2013
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