On Varieties and The Direct Limit of Groups

Document Type : Original Article

Author

Department of Mathematics, Islamic Azad university, Neyshabour branch, Neyshabour, Iran

Abstract

Leedham-Green and McKay [ Acta Math.137( 1967) 99-150] introduced the generalized version of the Baer-invariant of a group with respect to two varieties of groups. A group G is called capable if there exists a group H such that G=H/Z(H). In this paper , we generalize some properties of capability of direct product of groups with respect to two varieties of groups and direct Limits.Moreover, we survey some properties of the Baer - invariant of a pair of groups with respect to two varieties of groups and direct Limits.

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