# On centrally nilpotent loops

L. V. Safonova; K. K. Shchukin

Commentationes Mathematicae Universitatis Carolinae (2000)

- Volume: 41, Issue: 2, page 401-404
- ISSN: 0010-2628

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topSafonova, L. V., and Shchukin, K. K.. "On centrally nilpotent loops." Commentationes Mathematicae Universitatis Carolinae 41.2 (2000): 401-404. <http://eudml.org/doc/248585>.

@article{Safonova2000,

abstract = {Using a lemma on subnormal subgroups, the problem of nilpotency of multiplication groups and inner permutation groups of centrally nilpotent loops is discussed.},

author = {Safonova, L. V., Shchukin, K. K.},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {group; subnormal subgroup; loop; multiplication group; inner permutation group; commutative A-loops.; subnormal subgroups; centrally nilpotent loops; multiplication groups; inner permutation groups},

language = {eng},

number = {2},

pages = {401-404},

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

title = {On centrally nilpotent loops},

url = {http://eudml.org/doc/248585},

volume = {41},

year = {2000},

}

TY - JOUR

AU - Safonova, L. V.

AU - Shchukin, K. K.

TI - On centrally nilpotent loops

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 2000

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

VL - 41

IS - 2

SP - 401

EP - 404

AB - Using a lemma on subnormal subgroups, the problem of nilpotency of multiplication groups and inner permutation groups of centrally nilpotent loops is discussed.

LA - eng

KW - group; subnormal subgroup; loop; multiplication group; inner permutation group; commutative A-loops.; subnormal subgroups; centrally nilpotent loops; multiplication groups; inner permutation groups

UR - http://eudml.org/doc/248585

ER -

## References

top- Baer R., Abzählbar erkennbare gruppentheoretische Eigenschaften, Math. Z. 79 (1962), 344-363. (1962) Zbl0105.25901MR0148740
- Safonova L.V., Shchukin K.K., About n-Engel elements of groups, 12-th Algebr. Coll. of USSR, Thesis-book 1 Sverdlovsk (1973), 54. (1973)
- Smith J.D., Multiplication groups of quasigroups, Preprint 603, Technische Hochschule Darmstadt (1981). (1981)
- Bruck R.H., A Survey of Binary Systems, Springer-Verlag (1966). (1966) Zbl0141.01401MR0093552
- Shchukin K.K., On nilpotency of the multiplication group of an $A$-loop, Mat. Issled. 162 (1988), 116-117. (1988) Zbl0664.20043MR0947466
- Macdonald D., Neumann B.H., A third-Engel 5-group, J. Austral. Math. Soc. 7 (1967), 555-569. (1967) Zbl0163.02502MR0222171

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