# Affine regular decagons in GS-quasigroup

Vladimír Volenec; Zdenka Kolar-Begović

Commentationes Mathematicae Universitatis Carolinae (2008)

- Volume: 49, Issue: 3, page 383-395
- ISSN: 0010-2628

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topVolenec, Vladimír, and Kolar-Begović, Zdenka. "Affine regular decagons in GS-quasigroup." Commentationes Mathematicae Universitatis Carolinae 49.3 (2008): 383-395. <http://eudml.org/doc/23010>.

@article{Volenec2008,

abstract = {In this article the “geometric” concept of the affine regular decagon in a general GS–quasigroup is introduced. The relationships between affine regular decagon and some other geometric concepts in a general GS–quasigroup are explored. The geometrical presentation of all proved statements is given in the GS–quasigroup $\mathbb \{C\}(\frac\{1\}\{2\}(1+\sqrt\{5\}))$.},

author = {Volenec, Vladimír, Kolar-Begović, Zdenka},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {GS-quasigroup; affine regular decagon; affine regular pentagon; Moufang law; quasigroups; loops; laws of Bol-Moufang type; identities; quasigroup varieties},

language = {eng},

number = {3},

pages = {383-395},

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

title = {Affine regular decagons in GS-quasigroup},

url = {http://eudml.org/doc/23010},

volume = {49},

year = {2008},

}

TY - JOUR

AU - Volenec, Vladimír

AU - Kolar-Begović, Zdenka

TI - Affine regular decagons in GS-quasigroup

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 2008

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

VL - 49

IS - 3

SP - 383

EP - 395

AB - In this article the “geometric” concept of the affine regular decagon in a general GS–quasigroup is introduced. The relationships between affine regular decagon and some other geometric concepts in a general GS–quasigroup are explored. The geometrical presentation of all proved statements is given in the GS–quasigroup $\mathbb {C}(\frac{1}{2}(1+\sqrt{5}))$.

LA - eng

KW - GS-quasigroup; affine regular decagon; affine regular pentagon; Moufang law; quasigroups; loops; laws of Bol-Moufang type; identities; quasigroup varieties

UR - http://eudml.org/doc/23010

ER -

## References

top- Volenec V., GS-quasigroups, Časopis Pěst. Mat. 115 (1990), 307-318. (1990) Zbl0715.20044MR1071063
- Kolar Z., Volenec V., GS-trapezoids in GS-quasigroups, Math. Commun. 7 (2002), 143-158. (2002) Zbl1016.20052MR1952756
- Kolar-Begović Z., Volenec V., DGS-trapezoids in GS-quasigroups, Math. Commun. 8 (2003), 215-218. (2003) Zbl1061.20062MR2026399
- Kolar-Begović Z., Volenec V., Affine regular pentagons in GS-quasigroups, Quasigroups Related Systems 12 (2004), 103-112. (2004) Zbl1073.20062MR2130583
- Kolar-Begović Z., Volenec V., GS-deltoids in GS-quasigroups, Math. Commun. 10 (2005), 117-122. (2005) Zbl1089.20039MR2199101

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