On chirality groups and regular coverings of regular oriented hypermaps
نویسندگان
چکیده
منابع مشابه
Regular Oriented Hypermaps up to Five Hyperfaces
The chiral hypermaps with at most four hyperfaces were classified in [A. Breda d’Azevedo and R. Nedela,Chiral hypermaps with few hyperfaces, Math. Slovaca, 53 (2003), n.2, 107–128]. It arises from this classification that all chiral hypermaps are “canonical metacyclic”, that is, the one-step rotation about a hypervertex, or about a hyperedge, or about a hyperface, generates a normal subgroup in...
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An enumeration result for orientably-regular hypermaps of a given type with automorphism groups isomorphic to PSL(2, q) or PGL(2, q) can be extracted from a 1969 paper by Sah. We extend the investigation to orientable reflexible hypermaps and to non-orientable regular hypermaps, providing many more details about the associated computations and explicit generating sets for the associated groups.
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By adapting the notion of chirality group, the duality group of H can be defined as the the minimal subgroup D(H) E Mon(H) such that H/D(H) is a self-dual hypermap (a hypermap isomorphic to its dual). Here, we prove that for any positive integer d, we can find a hypermap of that duality index (the order of D(H)), even when some restrictions apply, and also that, for any positive integer k, we c...
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The regular coverings of regular affine algebraic maps are considered, and a large family of totally ramified coverings—the so-called Steinberg and Accola coverings—are fully classified.
متن کاملChirality groups of maps and hypermaps
Although the phenomenon of chirality appears in many investigations of maps and hypermaps, no detailed study of chirality seems to have been carried out. Chirality of maps and hypermaps is not merely a binary invariant but can be quantified by two new invariants—the chirality group and the chirality index, the latter being the size of the chirality group. A detailed investigation of the chirali...
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ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 2011
ISSN: 0011-4642,1572-9141
DOI: 10.1007/s10587-011-0046-6