Vol. 6, No. 4, 2013

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The probability of randomly generating finite abelian groups

Tyler Carrico

Vol. 6 (2013), No. 4, 431–436

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 pm pn, where m,n and  p is prime, is given, and the result is extended to groups of the form pn1 pnk, 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.

abelian, group, generate, probability
Mathematical Subject Classification 2010
Primary: 20P05
Received: 26 July 2012
Revised: 26 October 2012
Accepted: 13 November 2012
Published: 8 October 2013

Communicated by Joseph Gallian
Tyler Carrico
202-0004 Tokyo
Shimohoya 3-11-23