The Cayley graph and the growth of Steiner loops
P. Plaumann; L. Sabinina; I. Stuhl
Commentationes Mathematicae Universitatis Carolinae (2014)
- Volume: 55, Issue: 4, page 493-498
- ISSN: 0010-2628
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topPlaumann, P., Sabinina, L., and Stuhl, I.. "The Cayley graph and the growth of Steiner loops." Commentationes Mathematicae Universitatis Carolinae 55.4 (2014): 493-498. <http://eudml.org/doc/261994>.
@article{Plaumann2014,
abstract = {We study properties of Steiner loops which are of fundamental importance to develop a combinatorial theory of loops along the lines given by Combinatorial Group Theory. In a summary we describe our findings.},
author = {Plaumann, P., Sabinina, L., Stuhl, I.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {free Steiner loops; Cayley graph; growth; free Steiner loops; Cayley graphs; growth of loops},
language = {eng},
number = {4},
pages = {493-498},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {The Cayley graph and the growth of Steiner loops},
url = {http://eudml.org/doc/261994},
volume = {55},
year = {2014},
}
TY - JOUR
AU - Plaumann, P.
AU - Sabinina, L.
AU - Stuhl, I.
TI - The Cayley graph and the growth of Steiner loops
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2014
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 55
IS - 4
SP - 493
EP - 498
AB - We study properties of Steiner loops which are of fundamental importance to develop a combinatorial theory of loops along the lines given by Combinatorial Group Theory. In a summary we describe our findings.
LA - eng
KW - free Steiner loops; Cayley graph; growth; free Steiner loops; Cayley graphs; growth of loops
UR - http://eudml.org/doc/261994
ER -
References
top- Bruck R., Survey on Binary Systems, Ergebnisse der Mathematik und ihrer Grenzgebiete, Neue Folge, Heft 20, Reihe: Gruppentheorie, Springer, Berlin-Göttingen-Heidelberg, 1958. MR0093552
- Colbourn C.J., Dinitz J.H. (Eds.), Steiner Triple Systems, Section 4.5 in CRC Handbook of Combinatorial Designs, CRC Press, Boca Raton, FL, 1996, pp. 14–15 and 70. Zbl0984.05013
- Evans T., Varieties of loops and quasigroups, in Quasigroups and Loops: Theory and Applications, ed. O. Chein, H.O. Pflugfelder, J.D.H. Smith, Heldermann, Berlin, 1990, pp. 1–26. Zbl0721.20044MR1125807
- Flagolet P., Sedgewick R., Analytic Combinatorics, Cambridge University Press, Cambridge, 2009. MR2483235
- Ganter B., Pfüller U., 10.1007/BF01188065, Algebra Universalis 21 (1985), 310–311. Zbl0597.20065MR0855748DOI10.1007/BF01188065
- Grishkov A., Rasskazova D., Rasskazova M., Stuhl I., Free Steiner triple systems and their automorphism groups, J. Algebra Appl.(to appear).
- Mann A., How Groups Grow, Cambridge University Press, Cambridge, 2012. Zbl1253.20032MR2894945
- Markovski S., Sokolova A., Free Steiner loops, Glasnik Matematicki 36 (2001), 85–93. Zbl0978.08007MR1842827
- Mwambene E., 10.2989/16073600609486163, Quaest. Math. 29 (2006), 279–284. Zbl1107.05080MR2259722DOI10.2989/16073600609486163
- Pflugfelder H.O., Quasigroups and Loops: Introduction, Heldermann, Berlin, 1990. Zbl0715.20043MR1125767
- Sabidussi G., 10.1007/BF01304186, Monatsh. Math. 68 (1964), 426–438. Zbl0136.44608MR0175815DOI10.1007/BF01304186
- Strambach K., Stuhl I., 10.1016/j.disc.2008.12.019, Discrete Math. 309 (2009), 4225–4227. Zbl1194.20062MR2519154DOI10.1016/j.disc.2008.12.019
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