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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Goodaire, 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

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