@inproceedings{62611aac14914970b3e4dd749f065056,

title = "Enumeration of involutory latin quandles, bruck loops and commutative automorphic loops of odd prime power order",

abstract = ". There is a one-to-one correspondence between involutory latin quandles and uniquely 2-divisible Bruck loops. Bruck loops of odd prime power order are centrally nilpotent. Using linear-algebraic approach to central extensions, we enumerate Bruck loops (and hence involutory latin quandles) of order 3k for k ≤ 5, except for those loops that are central extensions of the cyclic group of order 3 by the elementary abelian group of order 34 . Among the constructed loops there is a Bruck loop of order 35 whose associated Γ-loop is not a commutative automorphic loop. We independently enumerate commutative automorphic loops of order 3k for k ≤ 5, with the same omission as in the case of Bruck loops.",

author = "Izabella Stuhl and Petr Vojt{\v e}chovsk{\'y}",

note = "Funding Information: 2010 Mathematics Subject Classification. Primary 57M27, 20N05. Key words and phrases. Quandle, latin quandle, involutory latin quandle, connected quandle, Bruck loop, Bol loop, Γ-loop, automorphic loop, commutative automorphic loop. The second author was partially supported by the University of Denver PROF grant.; 4th Mile High Conference on Nonassociative Mathematics, 2017 ; Conference date: 29-07-2017 Through 05-08-2017",

year = "2019",

doi = "10.1090/conm/721/14510",

language = "English (US)",

isbn = "9781470442453",

series = "Contemporary Mathematics",

publisher = "American Mathematical Society",

pages = "261--276",

editor = "Petr Vojtechovsk{\'y} and Bremner, {Murray R.} and {Scott Carter}, J. and Evans, {Anthony B.} and John Huerta and Kinyon, {Michael K.} and {Eric Moorhouse}, G. and Smith, {Jonathan D.H.}",

booktitle = "Nonassociative Mathematics and its Applications",

address = "United States",

}