# Loops which are cyclic extensions of their nuclei

Edgar G. Goodaire; D. A. Robinson

Compositio Mathematica (1982)

- Volume: 45, Issue: 3, page 341-356
- ISSN: 0010-437X

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topGoodaire, Edgar G., and Robinson, D. A.. "Loops which are cyclic extensions of their nuclei." Compositio Mathematica 45.3 (1982): 341-356. <http://eudml.org/doc/89540>.

@article{Goodaire1982,

author = {Goodaire, Edgar G., Robinson, D. A.},

journal = {Compositio Mathematica},

keywords = {normal subloops; weak-inverse loops; cyclic extension; nucleus; power- associative loop; Bol loop; loop-isotopes; finite G-loops; G-loops of composite orders},

language = {eng},

number = {3},

pages = {341-356},

publisher = {Martinus Nijhoff Publishers},

title = {Loops which are cyclic extensions of their nuclei},

url = {http://eudml.org/doc/89540},

volume = {45},

year = {1982},

}

TY - JOUR

AU - Goodaire, Edgar G.

AU - Robinson, D. A.

TI - Loops which are cyclic extensions of their nuclei

JO - Compositio Mathematica

PY - 1982

PB - Martinus Nijhoff Publishers

VL - 45

IS - 3

SP - 341

EP - 356

LA - eng

KW - normal subloops; weak-inverse loops; cyclic extension; nucleus; power- associative loop; Bol loop; loop-isotopes; finite G-loops; G-loops of composite orders

UR - http://eudml.org/doc/89540

ER -

## References

top- [1] V.D. Belousov: Foundations of the theory of quasigroups and loops (Russian), Izdat. "Nauka", Moskow, 1967. MR218483
- [2] R.H. Bruck: A survey of binary systems, Springer-Verlag, 1958. Zbl0141.01401MR93552
- [3] R.P. Burn: Finite Bol loops, Math. Proc. Cambridge Philos. Soc.84 (1978), no 3, 377-385. Zbl0385.20043MR492030
- [4] Orin Chein: Moufang loops of small order I., Trans. Amer. Math. Soc.188 (1974) 31-51. Zbl0286.20088MR330336
- [5] Edgar G. Goodaire and D.A. Robinson: A class of loops which are isomorphic to all loop isotopes, submitted. Zbl0467.20052
- [6] Marshall Hall, Jr.: The theory of groups, Macmillan, 1959. Zbl0084.02202MR103215
- [7] Harald Niederreiter and KAR L.H. Robinson: Bol loops of order pq, to appear. Zbl0463.20050MR600241
- [8] J. Marshall Osborn: Loops with the weak inverse property, Pacific J. Math.10 (1960) 295-304. Zbl0091.02101MR111800
- [9] D.A. Robinson: Bol loops, Trans. Amer. Math. Soc.123 (1966) 341-354. Zbl0163.02001MR194545
- [10] Eric L. Wilson: A class of loops with the isotopy-isomorphy property, Canad. J. Math.18 (1966) 589-592. Zbl0139.24702MR197614
- [11] Robert L. Wilson, Jr.: (a) Loop isotopism and isomorphism and extensions of universal algebras, Ph.D. Thesis, University of Wisconsin, Madison, 1969.(b) Isotopy-isomorphy loops of prime order, J. Algebra31 (1974) 117-119.(c) Quasidirect products of quasigroups, Comm. Algebra3(9) (1975) 835-850. Zbl0328.20067MR376937

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