Vol. 6, No. 4, 2013

Download this article
Download this article For screen
For printing
Recent Issues

Volume 7
Issue 6, 713–822
Issue 5, 585–712
Issue 4, 431–583
Issue 3, 245–430
Issue 2, 125–244
Issue 1, 1–124

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
Cover Page
Editorial Board
Editors' Addresses
Editors' Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Ethics Statement
Subscriptions
Editorial Login
Author Index
Coming Soon
Contacts
 
ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
The probability of randomly generating finite abelian groups

Tyler Carrico

Vol. 6 (2013), No. 4, 431–436
Abstract
[an error occurred while processing this directive]

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.

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

Communicated by Joseph Gallian
Authors
Tyler Carrico
202-0004 Tokyo
Nishitokyo-shi
Shimohoya 3-11-23
Japan