Das, PratulanandaSavaş, Ekrem2020-11-212020-11-2120151385-1292https://doi.org/10.1007/s11117-014-0282-8https://hdl.handle.net/11467/3732In this paper we continue in the line of recent investigation of order summability of nets using ideals by Boccuto et al. (Czechoslovak Math. J. 62(137):1073–1083 2012; J. Appl. Anal. 20(1), 2014) where they had introduced the notions of I and (Formula Presented.) order convergence, I and (Formula Presented.) divergence of nets and its further extensions, namely the notions of (Formula Presented.)-order convergence and (Formula Presented.)-divergence of nets in a (Formula Presented.)-group and investigate the relation between (Formula Presented.)-concepts where a special class of ideals called (Formula Presented.)-ideals plays very important role. We also introduce, for the first time, the notion of (Formula Presented.)-order Cauchy condition and (Formula Presented.)-order cluster points of nets in ((Formula Presented.)) groups and examine some of its characterizations and its consequences. In particular the role of (Formula Presented.)-order cluster points in making the above mentioned Cauchy nets convergent is studied. © 2014, Springer Basel.eninfo:eu-repo/semantics/closedAccess(?)-groupFilterI-divergenceI-order-cluster pointI-order-convergence/Cauchy conditionIK-divergenceIK-order-convergence/Cauchy conditionIdealNetArticle1915363Q3WOS:000351693900004Q22-s2.0-8489508495010.1007/s11117-014-0282-8