#### Filter Results:

#### Publication Year

2009

2017

#### Publication Type

#### Co-author

#### Publication Venue

#### Key Phrases

Learn More

We start by describing all the varieties of loops Q that can be defined by autotopisms αx, x ∈ Q, where αx is a composition of two triples, each of which becomes an autotopism when the element x belongs to one of the nuclei. In this way we obtain a unifying approach to Bol, Moufang, extra, Buchsteiner and conjugacy closed loops. We reprove some classical… (More)

We consider Murphy's polynomial selection algorithm for the general number field sieve. One of the steps in this algorithm consists of finding a minimum of an integral. However, the size of the polynomial coefficients causes the classical steepest descent algorithm to be ineffective. This article brings an idea how to improve the steepest descent algorithm… (More)

An automorphic loop (or A-loop) is a loop whose inner mappings are automorphisms. Every element of a commutative A-loop generates a group, and (xy) −1 = x −1 y −1 holds. Let Q be a finite commutative A-loop and p a prime. The loop Q has order a power of p if and only if every element of Q has order a power of p. The loop Q decomposes as a direct product of… (More)

- ‹
- 1
- ›