On finite commutative IP-loops with elementary abelian inner mapping groups of order p 5

Markku Niemenmaa

Commentationes Mathematicae Universitatis Carolinae (2020)

  • Volume: 61, Issue: 4, page 547-551
  • ISSN: 0010-2628

Abstract

top
We show that finite commutative inverse property loops with elementary abelian inner mapping groups of order p 5 are centrally nilpotent of class at most two.

How to cite

top

Niemenmaa, Markku. "On finite commutative IP-loops with elementary abelian inner mapping groups of order $p^5$." Commentationes Mathematicae Universitatis Carolinae 61.4 (2020): 547-551. <http://eudml.org/doc/297275>.

@article{Niemenmaa2020,
abstract = {We show that finite commutative inverse property loops with elementary abelian inner mapping groups of order $p^5$ are centrally nilpotent of class at most two.},
author = {Niemenmaa, Markku},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {loop; elementary abelian group; inner mapping group},
language = {eng},
number = {4},
pages = {547-551},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On finite commutative IP-loops with elementary abelian inner mapping groups of order $p^5$},
url = {http://eudml.org/doc/297275},
volume = {61},
year = {2020},
}

TY - JOUR
AU - Niemenmaa, Markku
TI - On finite commutative IP-loops with elementary abelian inner mapping groups of order $p^5$
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2020
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 61
IS - 4
SP - 547
EP - 551
AB - We show that finite commutative inverse property loops with elementary abelian inner mapping groups of order $p^5$ are centrally nilpotent of class at most two.
LA - eng
KW - loop; elementary abelian group; inner mapping group
UR - http://eudml.org/doc/297275
ER -

References

top
  1. Bruck R. H., 10.1090/S0002-9947-1946-0017288-3, Trans. Amer. Math. Soc. 60 (1946), 245–354. Zbl0061.02201MR0017288DOI10.1090/S0002-9947-1946-0017288-3
  2. Csörgö P., 10.1007/s00013-006-1379-5, Arch. Math. (Basel) 86 (2006), no. 6, 499–516. MR2241599DOI10.1007/s00013-006-1379-5
  3. Csörgö P., 10.1016/j.ejc.2005.12.002, European J. Combin. 28 (2007), no. 3, 858–867. Zbl1149.20053MR2300766DOI10.1016/j.ejc.2005.12.002
  4. Drápal A., Vojtěchovský P., 10.1016/j.ejc.2007.10.001, European J. Combin. 29 (2008), no. 7, 1662–1681. MR2431758DOI10.1016/j.ejc.2007.10.001
  5. Leppälä E., Niemenmaa M., On finite commutative loops which are centrally nilpotent, Comment. Math. Univ. Carolin. 56 (2015), no. 2, 139–143. Zbl1339.20064MR3338728
  6. Niemenmaa M., 10.1017/S0004972708001093, Bull. Aust. Math. Soc. 79 (2009), no. 1, 109–114. Zbl1167.20039MR2486887DOI10.1017/S0004972708001093
  7. Niemenmaa M., On finite commutative IP-loops with elementary abelian inner mapping groups of order p 4 , Comment. Math. Univ. Carolin. 51 (2010), no. 4, 559–563. MR2858260
  8. Niemenmaa M., On dihedral 2 -groups as inner mapping groups of finite commutative inverse property loops, Comment. Math. Univ. Carolin. 59 (2018), no. 2, 189–193. MR3815684
  9. Niemenmaa M., Kepka T., 10.1016/0021-8693(90)90152-E, J. Algebra 135 (1990), no. 1, 112–122. Zbl0706.20046MR1076080DOI10.1016/0021-8693(90)90152-E
  10. Niemenmaa M., Kepka T., 10.1017/S0004972700016166, Bull. Austral. Math. Soc. 49 (1994), no. 1, 121–128. Zbl0799.20020MR1262682DOI10.1017/S0004972700016166
  11. Niemenmaa M., Rytty M., Connected transversals and multiplication groups of loops, Quasigroups Related Systems 15 (2007), no. 1, 95–107. Zbl1133.20009MR2379127

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.