Computing the signatures of subgroups of non-Euclidean crystallographic groups
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DOI: 10.1016/j.jalgebra.2017.01.017
Abstract: Abstract A (planar and cocompact) non-Euclidean crystallographic (NEC) group Δ is a subgroup of the group of, conformal and anti-conformal, isometries of the hyperbolic plane H 2 such that H 2 / Δ is compact.… read more here.
Keywords: subgroups non; computing signatures; euclidean crystallographic; crystallographic groups ... See more keywords
Distinguishing crystallographic groups by their finite quotients
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DOI: 10.1016/j.jalgebra.2020.06.033
Abstract: Using the computer algebra program GAP, we show that all crystallographic groups in dimensions at most 4 are distinguished from each other by their sets of finite quotients. read more here.
Keywords: finite quotients; groups finite; distinguishing crystallographic; crystallographic groups ... See more keywords
WEAK CAYLEY TABLE GROUPS OF SOME CRYSTALLOGRAPHIC GROUPS
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DOI: 10.1017/s0017089517000337
Abstract: Abstract For a group G, a weak Cayley table isomorphism is a bijection f : G → G such that f(g1g2) is conjugate to f(g1)f(g2) for all g1, g2 ∈ G. The set of all… read more here.
Keywords: crystallographic groups; groups crystallographic; weak cayley; cayley table ... See more keywords