We show that the skew-symmetrized product on every Leib-niz algebra E can be realized on a reductive complement to a subalgebra in a Lie algebra. As a consequence, we construct a nonassociative… (More)

A loop whose inner mappings are automorphisms is an automorphic loop (or A-loop). We characterize commutative (A-)loops with middle nucleus of index 2 and solve the isomorphism problem. Using this… (More)

In the spirit of Glauberman’s fundamental work in B-loops and Moufang loops [18, 19], we prove Cauchy and strong Lagrange theorems for Bol loops of odd order. We also establish necessary conditions… (More)

Let Q be a conjugacy closed loop, and N(Q) its nucleus. Then Z(N(Q)) contains all associators of elements of Q. If in addition Q is diassociative (i.e., an extra loop), then all these associators… (More)

An A-loop is a loop in which every inner mapping is an automorphism. We settle a problem which had been open since 1956 by showing that every diassociative A-loop is Moufang.

We study a variety of loops, RIF, which arise naturally from considering the inner mapping group, and a somewhat larger variety, WRIF. All Steiner and Moufang loops are RIF, and all flexible C-loops… (More)

The “coquecigrue” problem for Leibniz algebras is that of finding an appropriate generalization of Lie’s third theorem, that is, of finding a generalization of the notion of group such that Leibniz… (More)

The panstochastic analogue of Birkhoff's Theorem on doubly-stochastic matrices is proved in the case n = 5. It is shown that this analogue fails when n > 1, n = 5.

We describe a large-scale project in applied automated deduction concerned with the following problem of considerable interest in loop theory: If Q is a loop with commuting inner mappings, does it… (More)