Abelian groups whose subgroup lattice is the union of two intervals

J. Aust. Math. Soc. 78 (2005), 27-36

Abelian groups whose subgroup lattice is the union of two intervals

Simion Breaz
Faculty of Mathematics
and Informatics
Babes-Bolyai University
Cluj-Napoca
Romania
bodo@math.ubbcluj.ro

and

Grigore Calugareanu
Dept. Mathematics and Computer Sci
Faculty of Science
Kuwait University
State of Kuwait
calu@mcs.sci.kuniv.edu.kw

Abstract

In this note we characterize the abelian groups

which have two different proper subgroups

and

such that the subgroup lattice $L(G)=[0,M]\cup [N,G]$ is the union of these intervals.