Atalan, FeriheMedetogullari, ElifOzan, YildirayMathematics2024-07-052024-07-05202130003-889X1420-893810.1007/s00013-020-01501-z2-s2.0-85095991255https://doi.org/10.1007/s00013-020-01501-zhttps://hdl.handle.net/20.500.14411/3210OZAN, YILDIRAY/0000-0003-2373-240X; Atalan, Ferihe/0000-0001-6547-0570We investigate branched regular finite abelian A-covers of the 2-sphere, where every homeomorphism of the base (preserving the branch locus) lifts to a homeomorphism of the covering surface. In this study, we prove that if A is a finite abelian p-group of rank k and Sigma -> S-2 is a regular A-covering branched over n points such that every homeomorphism f:S-2 -> S-2 lifts to Sigma, then n = k + 1. We will also give a partial classification of such covers for rank two finite p-groups. In particular, we prove that for a regular branched A-covering pi : Sigma -> S-2, where A = ZprxZpt, 1 <= r <= t , all homeomorphisms f:S-2 -> S-2 lift to those of Sigma if and only if t = r or t = r + 1 and p = 3.eninfo:eu-repo/semantics/closedAccessBranched coversMapping class groupAutomorphisms of groupsArticleQ3Q311613748WOS:000589153700001