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A Latin square, the unbordered multiplication table for a quasigroup whose 10 elements are the digits 0–9. The multiplication table of a finite quasigroup is a Latin square: an n × n table filled with n different symbols in such a way that each symbol occurs exactly once in each row and exactly once in each column.
A loop is universally flexible if every one of its loop isotopes is flexible, that is, satisfies (xy)x = x(yx). A loop is middle Bol if every one of its loop isotopes has the antiautomorphic inverse property, that is, satisfies (xy) −1 = y −1 x −1. Is there a finite, universally flexible loop that is not middle Bol?
In 493 AD, Victorius of Aquitaine wrote a 98-column multiplication table which gave (in Roman numerals) the product of every number from 2 to 50 times and the rows were "a list of numbers starting with one thousand, descending by hundreds to one hundred, then descending by tens to ten, then by ones to one, and then the fractions down to 1/144 ...
It requires memorization of the multiplication table for single digits. This is the usual algorithm for multiplying larger numbers by hand in base 10. A person doing long multiplication on paper will write down all the products and then add them together; an abacus-user will sum the products as soon as each one is computed.
Describe how all Latin subsquares in multiplication tables of Moufang loops arise. Proposed: by Aleš Drápal at Loops '03, Prague 2003; Comments: It is well known that every Latin subsquare in a multiplication table of a group G is of the form aH x Hb, where H is a subgroup of G and a, b are elements of G.
In its most general form a loop group is a group of continuous mappings from a manifold M to a topological group G.. More specifically, [1] let M = S 1, the circle in the complex plane, and let LG denote the space of continuous maps S 1 → G, i.e.
Use a non-breaking space with or {} in empty cells to maintain the table structure. Custom CSS styling: Override the wikitable class defaults by explicitly specifying: border-collapse: collapse; border: none; Apply these styles to the table or specific cells using inline styles or a custom class.
The group scheme of n-th roots of unity is by definition the kernel of the n-power map on the multiplicative group GL(1), considered as a group scheme.That is, for any integer n > 1 we can consider the morphism on the multiplicative group that takes n-th powers, and take an appropriate fiber product of schemes, with the morphism e that serves as the identity.