Extending the structural homomorphism of LCC loops
Commentationes Mathematicae Universitatis Carolinae (2005)
- Volume: 46, Issue: 3, page 385-389
- ISSN: 0010-2628
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topCsörgö, Piroska. "Extending the structural homomorphism of LCC loops." Commentationes Mathematicae Universitatis Carolinae 46.3 (2005): 385-389. <http://eudml.org/doc/249566>.
@article{Csörgö2005,
abstract = {A loop $Q$ is said to be left conjugacy closed if the set $A=\lbrace L_x/x\in Q\rbrace $ is closed under conjugation. Let $Q$ be an LCC loop, let $\mathcal \{L\}$ and $\mathcal \{R\}$ be the left and right multiplication groups of $Q$ respectively, and let $I(Q)$ be its inner mapping group, $M(Q)$ its multiplication group. By Drápal’s theorem [3, Theorem 2.8] there exists a homomorphism $\Lambda : \mathcal \{L\} \rightarrow I(Q)$ determined by $L_x\rightarrow R^\{-1\}_x L_x$. In this short note we examine different possible extensions of this $\Lambda $ and the uniqueness of these extensions.},
author = {Csörgö, Piroska},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {LCC loop; multiplication group; inner mapping group; homomorphism; left conjugacy closed loops; multiplication groups; inner mapping groups; homomorphisms},
language = {eng},
number = {3},
pages = {385-389},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Extending the structural homomorphism of LCC loops},
url = {http://eudml.org/doc/249566},
volume = {46},
year = {2005},
}
TY - JOUR
AU - Csörgö, Piroska
TI - Extending the structural homomorphism of LCC loops
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2005
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 46
IS - 3
SP - 385
EP - 389
AB - A loop $Q$ is said to be left conjugacy closed if the set $A=\lbrace L_x/x\in Q\rbrace $ is closed under conjugation. Let $Q$ be an LCC loop, let $\mathcal {L}$ and $\mathcal {R}$ be the left and right multiplication groups of $Q$ respectively, and let $I(Q)$ be its inner mapping group, $M(Q)$ its multiplication group. By Drápal’s theorem [3, Theorem 2.8] there exists a homomorphism $\Lambda : \mathcal {L} \rightarrow I(Q)$ determined by $L_x\rightarrow R^{-1}_x L_x$. In this short note we examine different possible extensions of this $\Lambda $ and the uniqueness of these extensions.
LA - eng
KW - LCC loop; multiplication group; inner mapping group; homomorphism; left conjugacy closed loops; multiplication groups; inner mapping groups; homomorphisms
UR - http://eudml.org/doc/249566
ER -
References
top- Basarab A.S., A class of LK-loops (in Russian), Mat. Issled. 120 (1991), 3-7. (1991) MR1121425
- Drápal A., Conjugacy closed loops and their multiplication groups, J. Algebra 272 (2004), 838-850. (2004) Zbl1047.20049MR2028083
- Drápal A., On multiplication groups of left conjugacy closed loops, Comment. Math. Univ. Carolinae 45 (2004), 223-236. (2004) Zbl1101.20035MR2075271
- Goodaire E.G., Robinson D.A., A class of loops which are isomorphic to all loop isotopes, Canad. J. Math. 34 (1982), 662-672. (1982) Zbl0467.20052MR0663308
- Kiechle H., Nagy G.P., On the extension of involutorial Bol loops, Abh. Math. Sem. Univ. Hamburg 72 (2002), 235-250. (2002) Zbl1016.20051MR1941556
- Nagy P., Strambach K., Loops as invariant sections in groups and their geometry, Canad. J. Math. 46 (1994), 1027-1056. (1994) Zbl0814.20055MR1295130
- Soikis L.R., The special loops (in Russian), in: Voprosy teorii kvazigrupp i lup (V.D. Belousov, ed.), Akademia Nauk Moldav. SSR, Kishinyev, 1970, pp.122-131. MR0281828
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