A Note on the Universal Factorization Property of Groups

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We give criteria when a full subcategory D of the category of groups has C-universal factorization property (C-UFP) or C-strong universal factorization property(C-SUFP) for a certain category of groups C.As a byproduct,we give affirmative answers to three unsettled questions in[S.W.Kim,J.B.Lee,Universal factorization property of certain polycyclic groups,J.Pure Appl.Algebra 204 (2006) 555-567].
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