A theory of restricted regularity of hypermaps
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Abstract
and are a generalisation of maps, that is, 2-cellulardecompositions of closed surfaces. There is a well knowncorrespondence between hypermaps and co-compact subgroups of thefree product Delta=C_2*C_2*C_2. In this correspondence,hypermaps correspond to conjugacy classes of subgroups ofDelta, and hypermap coverings to subgroup inclusions. Towardsthe end of cite{BNjih} the authors studied regular hypermaps withextra symmetries, namely, G-symmetric regular hypermaps for anysubgroup G of the outer automorphism mbox{Out}(Delta) of thetriangle group Delta. This can be viewed as an extension of thetheory of regularity. In this paper we move in the oppositedirection and restrict regularity to normal subgroups Theta ofDelta of finite index. This generalises the notion ofregularity to some non-regular objects.
참고문헌 (23)
- "Self-dual regular maps from medial graphs", pp.57~ (1992), ActaMath. Univ. Comenian.} 61
- "On Galois extensions of a maximalcyclotomic field", pp.247~ (1980)
- "Regular maps on an anchorring", pp.225~ (1926)
- "The Reflexible Hypermaps ofCharacteristic -2", 47(2), pp.131~153 (1997)
- "Doublecoverings and reflexible abelian hypermaps", 41(2), pp.371~389 (2000)
- A.Breda d'Azevedo, "Chirality groups of maps and hypermaps"
- A.Breda d'Azevedo, "Chiral hypermapsof small genus", 44(1), pp.127~143 (2003)
- "Chiral hypermaps with fewhyperfaces", 53(2), pp.107~128 (2003)
- "Join and Intersection of hypermaps", (9), pp.13~28 (2001)
- "Foundations of thetheory of maps on surfaces with boundary", pp.17~36 (1985)
- "Theory of groups of finite order" (1955)
- "Locally finite,planar, edge-transitive graphs", 126(601) (1997)
- "Esquisse d'un programme", pp.1 243~ (1984), 242}Cambridge Univ. Press}
- "Algebraic Methods in Graph Theory", pp.297~ (1978), North-Holland
- "Maps on surfaces and Galois groups", 47(1), pp.1~33 (1997)
- "Theory of maps onorientable surfaces", pp.273~ (1978)
- "Belybri functions, hypermaps and Galoisgroups", 28(6), pp.561~590 (1996)
- "Regular maps --- combinatorialobjects relating different fields of mathematics", 38(5), pp.1069~1105 (2001)
- "Automorphisms of maps", pp.65~8 (1976)
- "Triangle grouprepresentations and constructions of regular maps", 82(3), pp.513~532 (2001)
- "Realizing finite edge-transitive orientable maps", 37(1), pp.1~34 (2001)
- "New Techniques for theConstruction of Regular Maps University of Washington}" (1976)
- "Theory of Groups" (1958), ChelseaPublishing Company