# A class of latin squares derived from finite abelian groups

Commentationes Mathematicae Universitatis Carolinae (2014)

- Volume: 55, Issue: 3, page 401-409
- ISSN: 0010-2628

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topEvans, Anthony B.. "A class of latin squares derived from finite abelian groups." Commentationes Mathematicae Universitatis Carolinae 55.3 (2014): 401-409. <http://eudml.org/doc/261868>.

@article{Evans2014,

abstract = {We consider two classes of latin squares that are prolongations of Cayley tables of finite abelian groups. We will show that all squares in the first of these classes are confirmed bachelor squares, squares that have no orthogonal mate and contain at least one cell though which no transversal passes, while none of the squares in the second class can be included in any set of three mutually orthogonal latin squares.},

author = {Evans, Anthony B.},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {latin squares; bachelor squares; monogamous squares; prolongation; Latin square; bachelor square; confirmed bachelor square; monogamous square; prolongation},

language = {eng},

number = {3},

pages = {401-409},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {A class of latin squares derived from finite abelian groups},

url = {http://eudml.org/doc/261868},

volume = {55},

year = {2014},

}

TY - JOUR

AU - Evans, Anthony B.

TI - A class of latin squares derived from finite abelian groups

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 2014

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 55

IS - 3

SP - 401

EP - 409

AB - We consider two classes of latin squares that are prolongations of Cayley tables of finite abelian groups. We will show that all squares in the first of these classes are confirmed bachelor squares, squares that have no orthogonal mate and contain at least one cell though which no transversal passes, while none of the squares in the second class can be included in any set of three mutually orthogonal latin squares.

LA - eng

KW - latin squares; bachelor squares; monogamous squares; prolongation; Latin square; bachelor square; confirmed bachelor square; monogamous square; prolongation

UR - http://eudml.org/doc/261868

ER -

## References

top- Belyavskaya G.B., Generalized extension of quasigroups, (Russian), Mat. Issled. 5 (1970), 28–48. MR0284533
- Belyavskaya G.B., Contraction of quasigroups. I., (Russian), Bul. Akad. Stiince RSS Moldoven (1970), 6–12. MR0279219
- Belyavskaya G.B., Contraction of quasigroups. II., (Russian), Bul. Akad. Stiince RSS Moldoven (1970), 3–17. MR0284531
- Danziger P., Wanless I.M., Webb B.S., 10.1016/j.jcta.2010.11.011, J. Combin. Theory Ser. A 118 (2011), 796–807. Zbl1232.05033MR2745425DOI10.1016/j.jcta.2010.11.011
- Deriyenko I.I., Dudek W.A., On prolongation of quasigroups, Quasigroups and Related Systems 16 (2008), 187–198. MR2494876
- Evans A.B., 10.1007/s10623-006-8153-3, Des. Codes Crypt. 40 (2006), 121–130. Zbl1180.05022MR2226287DOI10.1007/s10623-006-8153-3
- Paige L.J., 10.1090/S0002-9904-1947-08842-X, Bull. Amer. Math. Soc. 53 (1947), 590–593. Zbl0033.15101MR0020990DOI10.1090/S0002-9904-1947-08842-X
- Wanless I.M., Transversals in latin squares: a survey, Surveys in combinatorics 2011, pp. 403–437, London Math. Soc. Lecture Note Ser., 392, Cambridge Univ. Press, Cambridge, 2011. Zbl1226.05067MR2866738
- Wanless I.M., Webb B.S., 10.1007/s10623-006-8168-9, Des. Codes Cryptogr. 40 (2006), 131–135. Zbl1180.05023MR2226288DOI10.1007/s10623-006-8168-9

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