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Discrete Subgroups of the Euclidean Group
2001Since the Euclidean group \(\mathbb{E}\) has continuously many elements: $$ \left| \mathbb{E} \right| = \left| \mathbb{R} \right| = c, $$ it has 2csubsets, and each of these generates a subgroup. So, to avoid bewilderment, it is necessary to place some restriction on the class of subgroups to be investigated.
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Discretization in Subgroup Discovery
2016Subgroup discovery is a data mining technique to discoverer interesting subgroups from a selected population. It seeks to discover interesting relationships between different objects in a set with respect to a specific property. The discovered patterns are called subgroups and they are represented in the form of rules.
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Discreteness of lattices of closed subgroups of lie groups
Ukrainian Mathematical Journal, 1986Let G be a locally compact group and let L(G) be the set of all closed subgroups of G. The family \(\{\) \(F\in L(G) :\) \(H\subseteq F\subseteq HU\}\) forms the base of a topology \(\tau\) on L(G) (H\(\in L(G)\), U runs over a neighbourhood base of unit of G). It is proved that the space \(L_{\tau}(G)\) is discrete iff G is a Lie group.
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A Note on Subgroup Security in Discrete Logarithm-Based Cryptography
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2021Tadanori Teruya
exaly
On Subgroups with Property (P) and Maximal Discrete Subgroups
American Journal of Mathematics, 1975openaire +1 more source
A note on groups with a large permodularly embedded subgroup
Beitrage Zur Algebra Und Geometrie, 2023Francesco De Giovanni +2 more
exaly
Orthogonality and additivity modulo a discrete subgroup
Aequationes Mathematicae, 2005Karol Baron
exaly