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Paper   IPM / M / 629
School of Mathematics
  Title:   The category P M E (G, V) and generalized covering groups
  Author(s):  S. Kayvanfar
  Status:   Published
  Journal: J. Algebra
  No.:  1
  Vol.:  238
  Year:  2001
  Pages:   126-138
  Supported by:  IPM
The properties of covering and universality between the central extensions and the structure of a covering group of perfect groups have been generalized by S. Kayvanfar and M. R. R. Moghaddam (1997, Indag. Math. N.S. 8(4), 537-542) to the variety of groups defined by a set of outer commutator words. In this paper we generalize the above results to any variety of groups. Then we introduce the category P M E (G, V) and, using the above generalization, show that if G is V-perfect, then there exists a universal object in this category and its structure will be determined. Finally it is shown that any two V-covering groups of a V-perfect group are isomorphic and the structure of the unique generalized covering group of an arbitrary V-perfect group is introduced.

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