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