mathematics, a Moufang loop is a special kind of algebraic structure. It is similar to a group in many ways but need not be associative. Moufang loops were introduced...

(commutative) Moufang loop L of order 81 with normal commutative subgroup of order 27. Conjecture: Any finite commutative Moufang loop of period 3 can...

right Bol loop). A loop that is both a left and right Bol loop is a Moufang loop. This is equivalent to any one of the following single Moufang identities...

In geometry, a Moufang plane, named for Ruth Moufang, is a type of projective plane, more specifically a special type of translation plane. A translation...

concepts in mathematics are named: Moufang–Lie algebra Moufang loop Moufang polygon Moufang plane Moufang set David Moufang (born 1966), German ambient techno...

group forms a Lie algebra, the tangent space of the identity of a smooth Moufang loop forms a Malcev algebra. Moreover, just as a Lie group can be recovered...

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...

Ruth Moufang (10 January 1905 – 26 November 1977) was a German mathematician. She was born to German chemist Eduard Moufang and Else Fecht Moufang. Eduard...

\mathbb {O} \ } do not form a group. They do, however, form a loop, specifically a Moufang loop. The commutator of two octonions x and y is given by [ x ...

alternativity. A loop is both left Bol and right Bol if and only if it is a Moufang loop. Alternatively, a right or left Bol loop is Moufang if and only if...

associative and therefore alternative. Moufang loops are alternative and flexible but not associative. See Moufang loop § Examples for more examples. Octonion...

Moreover, the Moufang identities hold in any octonion algebra. It follows that the invertible elements in any octonion algebra form a Moufang loop, as do the...

lattices and deep holes of the Leech lattice, and constructed Parker's Moufang loop of order 213 (which was used by John Horton Conway in his construction...

In mathematics, Moufang polygons are a generalization by Jacques Tits of the Moufang planes studied by Ruth Moufang, and are irreducible buildings of...

elements is therefore closed under multiplication and forms a Moufang loop. This loop of units in an alternative ring or algebra is analogous to the...

includes many important classes of magmas: all groups, semigroups and moufang loops are flexible. The sedenions and trigintaduonions, and all algebras constructed...

multiplication operation making them not into a group but rather a loop, in fact a Moufang loop. For visualization this 8-dimensional polytope is often displayed...

invertible elements (i.e. those elements for which N(x) ≠ 0) form a Moufang loop. The automorphism group of the split-octonions is a 14-dimensional Lie...

1971, ISBN 978-0-387-03497-3) Bruck, R. H. (1960), "Some theorems on Moufang loops", Math. Z., 73 (1): 59–78, doi:10.1007/bf01163269, S2CID 121239766 Bruck...

non-abelian CH-quasigroups and to describe the structure of commutative Moufang loops of exponent 3. Suppose that G is a group that is generated by a conjugacy...

intuitionistic logician Ruth Moufang (1905–1977), German researcher on non-associative algebraic structures, namesake of Moufang loops Magdalena Mouján (1926–2005)...

Notices of the AMS, 54 (10): 1294–1303 Near-field Semifield Alternative division ring Hall systems (Hall planes) Moufang plane Quasifields by Hauke Klein....

same octonion and is unambiguously defined due to octonions obeying the Moufang identities). It can be shown that an element of SO(8) can be constructed...

the original on 2016-03-05. Retrieved 2015-09-01. See Magnus, Wilhelm; Moufang, Ruth (1954). "Max Dehn zum Gedächtnis". Mathematische Annalen. 127 (1):...

representation theory) Maschke's theorem (group representations) Moufang's theorem (loop theory) Nielsen–Schreier theorem (free groups) Orbit-stabilizer...