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
Discrete groups without finite quotients
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DOI: 10.1016/j.topol.2018.08.013
Abstract: We construct an infinite discrete subgroup of the isometry group of $\mathbb H^3$ with no finite quotients other than the trivial group. read more here.
Keywords: groups without; topology; without finite; finite quotients ... See more keywords
Distinguishing Some Genus One Knots Using Finite Quotients
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DOI: 10.1142/s0218216523500359
Abstract: We give a criterion for distinguishing a prime knot $K$ in $S^3$ from every other knot in $S^3$ using the finite quotients of $\pi_1(S^3\setminus K)$. Using recent work of Baldwin-Sivek, we apply this criterion to… read more here.
Keywords: distinguishing genus; finite quotients; using finite; one knots ... See more keywords