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arXiv:1312.1485 [math.GR]AbstractReferencesReviewsResources

Subgroups of finite Abelian groups having rank two via Goursat's lemma

László Tóth

Published 2013-12-05, updated 2014-09-23Version 2

Using Goursat's lemma for groups, a simple representation and the invariant factor decompositions of the subgroups of the group Z_m x Z_n are deduced, where m and n are arbitrary positive integers. As consequences, explicit formulas for the total number of subgroups, the number of subgroups with a given invariant factor decomposition, and the number of subgroups of a given order are obtained.

Comments: 9 pages, revised, new results added, 1 figure, 1 table
Categories: math.GR, math.CO, math.NT
Subjects: 20K01, 20K27, 11A25
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