The classification of finite simple Moufang loops
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Publication:3759053
DOI10.1017/S0305004100067025zbMath0622.20061OpenAlexW2157468340MaRDI QIDQ3759053
Publication date: 1987
Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1017/s0305004100067025
finite simple groupsfinite simple Moufang loopsCayley algebrasfinite simple non-associative Moufang loops
Loops, quasigroups (20N05) Finite simple groups and their classification (20D05) Alternative rings (17D05) Nonassociative division algebras (17A35)
Related Items (52)
Toward the classification of Moufang loops of order 64. ⋮ Incidence properties of cosets in loops ⋮ Lie bialgebras with triality and Mal'tsev bialgebras ⋮ On linear repkesentations of moufang loops ⋮ Embedding of strongly simple Moufang loops in simple alternative algebras ⋮ The maximal subloops of the simple Moufang loop of order 1080. ⋮ Maximal subloops of finite simple Moufang loops. ⋮ The group PSL(2,q) is not the multiplication group of a loop ⋮ On connected transversals to Abelian subgroups ⋮ Unnamed Item ⋮ Embedding Mal'tsev coalgebras into Lie coalgebras with triality ⋮ Problems on structure of finite quasifields and projective translation planes ⋮ The geometry of diagonal groups ⋮ Incidence geometries with trialities coming from maps with Wilson trialities ⋮ Criteria for solvable radical membership via \(p\)-elements. ⋮ On loops which have dihedral 2-groups as inner mapping groups ⋮ On abelian-by-cyclic Moufang loops ⋮ All f-loops are groups ⋮ Loops and the Lagrange property. ⋮ Abelian congruences and solvability in Moufang loops ⋮ Generation of finite almost simple groups by conjugates. ⋮ Coverings of the smallest Paige loop. ⋮ Characterizations of the solvable radical ⋮ On the non-commuting graph in finite Moufang loops ⋮ Bol loops and Bruck loops of order \(pq\) ⋮ The smallest simple Moufang loop. ⋮ The Number of Sylowp-Subloops in Finite Moufang Loops ⋮ Central reflections and nilpotency in exact Mal'tsev categories ⋮ A description of Baer-Suzuki type of the solvable radical of a finite group. ⋮ Further solvable analogues of the Baer-Suzuki theorem and generation of nonsolvable groups. ⋮ The finite Bruck loops. ⋮ On Bol loops of exponent 2. ⋮ Generators of nonassociative simple Moufang loops over finite prime fields ⋮ Hall's theorem for Moufang loops. ⋮ On the smallest simple, unipotent Bol loop. ⋮ CLASSIFICATION OF SUBALGEBRAS OF THE CAYLEY ALGEBRA OVER A FINITE FIELD ⋮ On point stabilizers in primitive permutation groups ⋮ On the group \(\mathrm{PSL}(n,q)\) as the multiplication group of a loop. ⋮ Half-automorphisms of simple Moufang loops ⋮ Direct construction of code loops. ⋮ The conjugacy of triality subgroups of Sylow subloops of Moufang loops ⋮ The existence of Sylow 2-subloops in finite Moufang loops. ⋮ The development of Sylow \(p\)-subloops in finite Moufang loops. ⋮ A class of simple proper Bol loops. ⋮ Sylow's theorem for Moufang loops. ⋮ Moufang Loops and Groups with Triality are Essentially the Same Thing ⋮ GROUPS WITH TRIALITY ⋮ On the number of elements which are not n-th powers in finite groups ⋮ Abelian-by-Cyclic Moufang Loops ⋮ On subloops of the loop of invertible elements in the split Cayley–Dickson algebra over a field ⋮ Simple Bol Loops ⋮ Unnamed Item
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