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| Paper IPM / M / 629 |
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| Abstract: | |
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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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