Journal of Advanced Research in Pure Mathematics, Volume (4), No (3), Year (2012-8) , Pages (1-7)

Title : ( On Varietal Capability of Direct Products of Groups and Pairs of Groups )

Authors: Bibi Hanieh Mirebrahimi Paziquee , Behrooz Mashayekhy Fard ,
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Abstract

In this paper we give some conditions in which a direct product of groups is V−capable if and only if each of its factors is V−capable for some varieties V. Moreover, we give some conditions in which a direct product of a finite family of pairs of groups is capable if and only if each of its factors is a capable pair of groups.

Keywords

, Capable group; Direct product; Variety of groups; V−capable group, Pair of groups; Capable pair of groups