On finite commutative IP-loops with elementary abelian inner mapping groups of order p 4

Markku Niemenmaa

Commentationes Mathematicae Universitatis Carolinae (2010)

  • Volume: 51, Issue: 4, page 559-563
  • ISSN: 0010-2628

Abstract

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We show that finite commutative inverse property loops with elementary abelian inner mapping groups of order p 4 are centrally nilpotent of class at most two.

How to cite

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Niemenmaa, Markku. "On finite commutative IP-loops with elementary abelian inner mapping groups of order $p^4$." Commentationes Mathematicae Universitatis Carolinae 51.4 (2010): 559-563. <http://eudml.org/doc/246340>.

@article{Niemenmaa2010,
abstract = {We show that finite commutative inverse property loops with elementary abelian inner mapping groups of order $p^4$ are centrally nilpotent of class at most two.},
author = {Niemenmaa, Markku},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {loop; inner mapping group; finite commutative inverse property loops; inner mapping groups; centrally nilpotent loops; multiplication groups; connected transversals},
language = {eng},
number = {4},
pages = {559-563},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On finite commutative IP-loops with elementary abelian inner mapping groups of order $p^4$},
url = {http://eudml.org/doc/246340},
volume = {51},
year = {2010},
}

TY - JOUR
AU - Niemenmaa, Markku
TI - On finite commutative IP-loops with elementary abelian inner mapping groups of order $p^4$
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2010
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 51
IS - 4
SP - 559
EP - 563
AB - We show that finite commutative inverse property loops with elementary abelian inner mapping groups of order $p^4$ are centrally nilpotent of class at most two.
LA - eng
KW - loop; inner mapping group; finite commutative inverse property loops; inner mapping groups; centrally nilpotent loops; multiplication groups; connected transversals
UR - http://eudml.org/doc/246340
ER -

References

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  5. Kepka T., Niemenmaa M., 10.1016/0021-8693(90)90152-E, J. Algebra 135 (1990), 112–122. (1990) Zbl0706.20046MR1076080DOI10.1016/0021-8693(90)90152-E
  6. Kepka T., Niemenmaa M., 10.1112/blms/24.4.343, Bull. London Math. Soc. 24 (1992), 343–346. (1992) Zbl0793.20064MR1165376DOI10.1112/blms/24.4.343
  7. Kepka T., Niemenmaa M., 10.1017/S0004972700016166, Bull. Australian Math. Soc. 49 (1994), 121–128. (1994) Zbl0799.20020MR1262682DOI10.1017/S0004972700016166
  8. Kinyon M., private communication, 2009. 
  9. Niemenmaa M., 10.1017/S0004972700038491, Bull. Australian Math. Soc. 71 (2005), 487–492. (2005) Zbl1080.20061MR2150938DOI10.1017/S0004972700038491
  10. Niemenmaa M., Rytty M., Connected transversals and multiplication groups of loops, Quasigroups and Related Systems 15 (2007), 95–107. (2007) Zbl1133.20009MR2379127

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