whatisbad.blogg.se - Wolfram mathematica for loop

Proposed: by Tomáš Kepka and Petr Němec at Loops '03, Prague 2003.

Is the variety of loops a minimal isotopically universal variety? Does every isotopically universal variety contain the variety of loops or its parastrophes? Minimal isotopically universal varieties of quasigroups Ī variety V of quasigroups is isotopically universal if every quasigroup is isotopic to a member of V.

Proposed: by Jaroslav Ježek and Tomáš Kepka at Loops '03, Prague 2003.

Open problems (quasigroups) Existence of infinite simple paramedial quasigroups Īre there infinite simple paramedial quasigroups?

Comment: There is a finite loop with no finite basis for its laws (Vaughan-Lee, 1979) but it is not nilpotent.

Vaughan-Lee in the Kourovka Notebook of Unsolved Problems in Group Theory

Comment: The counts are known for n < 24, see (Daly and Vojtěchovský, 2010).Ī finite nilpotent loop without a finite basis for its laws Ĭonstruct a finite nilpotent loop with no finite basis for its laws.

Proposed: by Petr Vojtěchovský at the 2nd Mile High Conference on Nonassociative Mathematics, Denver 2009.

Number of nilpotent loops up to isomorphism ĭetermine the number of nilpotent loops of order 24 up to isomorphism. Minimal presentations for loops M(G,2) įor a group G from the class satisfying d ( ∗, + ) 3 (Nagy and Vojtěchovský, 2007).

Proposed: by Alexander Grishkov at Loops '11, Třešť 2011.Then Φ( L) is a normal nilpotent subloop of L. Proposed: by Alexander Grishkov at Loops '03, Prague 2003įrattini subloop for Moufang loops Ĭonjecture: Let L be a finite Moufang loop and Φ( L) the intersection of all maximal subloops of L.Comments: The assumption that L/ M has order bigger than 3 is important, as there is a (commutative) Moufang loop L of order 81 with normal commutative subgroup of order 27.Įmbedding CMLs of period 3 into alternative algebras Ĭonjecture: Any finite commutative Moufang loop of period 3 can be embedded into a commutative alternative algebra.Proposed: by Michael Kinyon, based on (Chein and Rajah, 2000).(i) Is L a group? (ii) If the orders of M and L/ M are relatively prime, is L a group? Let L be a Moufang loop with normal abelian subgroup (associative subloop) M of odd order such that L/ M is a cyclic group of order bigger than 3.

Open problems (Moufang loops) Abelian by cyclic groups resulting in Moufang loops Many of the problems posed here first appeared in the Loops (Prague) conferences and the Mile High (Denver) conferences. As in other areas of mathematics, such problems are often made public at professional conferences and meetings. In mathematics, especially abstract algebra, loop theory and quasigroup theory are active research areas with many open problems.