12 citations · 42 across the 11 of their papers we have counts for
7 papers · 1 filter
Commutative automorphic loops of order
Dylene Agda Souza de Barros, Alexander Grishkov, Petr Vojtěchovský
A loop is said to be automorphic if its inner mappings are automorphisms. For a prime , denote by the class of all -generated commutative automorphic loops …
Enumeration of nilpotent loops via cohomology
Daniel Daly, Petr Vojtěchovský
The isomorphism problem for centrally nilpotent loops can be tackled by methods of cohomology. We develop tools based on cohomology and linear algebra that either lend themselves t…
Moufang loops with commuting inner mappings
Gábor P. Nagy, Petr Vojtěchovský
We investigate the relation between the structure of a Moufang loop and its inner mapping group. Moufang loops of odd order with commuting inner mappings have nilpotency class at m…
Overlapping latin subsquares and full products
Joshua M. Browning, Petr Vojtěchovský, Ian M. Wanless
We derive necessary and sufficient conditions for there to exist a latin square of order containing two subsquares of order and that intersect in a subsquare of order $…
The free commutative automorphic -generated loop of nilpotency class
Dylene Agda Souza de Barros, Alexander Grishkov, Petr Vojtěchovský
A loop is automorphic if all its inner mappings are automorphisms. We construct the free commutative automorphic -generated loop of nilpotency class . It has dimension ov…
A scoop from groups: Equational foundations for loops
J. D. Phillips, Petr Vojtěchovský
Groups are usually axiomatized as algebras with an associative binary operation, a two-sided neutral element, and with two-sided inverses. We show in this note that the same simpli…
Computing with small quasigroups and loops
Gábor P. Nagy, Petr Vojtěchovský
This is a companion to our lectures GAP and loops, to be delivered at the Workshops Loops 2007, Prague, Czech Republic. In the lectures we introduce the GAP package LOOPS, describe…