Primary decomposition for $Sigma$-groups

Don Brunker, Denis Higgs
1988 Canadian mathematical bulletin  
A 2-group is an abelian group on which is given a collection of infinite sums having properties suggested by those of absolutely convergent series in R or C. It is shown that the usual decomposition of a torsion abelian group into its /7-components carries over to the case of 2-groups when the property of being torsion is replaced by an appropriate uniform version. For a certain class of 2-groups, it turns out that being torsion is already sufficient for primary decomposition to hold.
doi:10.4153/cmb-1988-057-2 fatcat:zmhxjkbbtzcpbpl2bt3bipzq4y