On the structure of finite loop capable nilpotent groups

Miikka Rytty

Commentationes Mathematicae Universitatis Carolinae (2010)

  • Volume: 51, Issue: 2, page 349-355
  • ISSN: 0010-2628

Abstract

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In this paper we consider finite loops and discuss the problem which nilpotent groups are isomorphic to the inner mapping group of a loop. We recall some earlier results and by using connected transversals we transform the problem into a group theoretical one. We will get some new answers as we show that a nilpotent group having either C p k × C p l , k > l ≥ 0 as the Sylow p -subgroup for some odd prime p or the group of quaternions as the Sylow 2 -subgroup may not be loop capable.

How to cite

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Rytty, Miikka. "On the structure of finite loop capable nilpotent groups." Commentationes Mathematicae Universitatis Carolinae 51.2 (2010): 349-355. <http://eudml.org/doc/37765>.

@article{Rytty2010,
abstract = {In this paper we consider finite loops and discuss the problem which nilpotent groups are isomorphic to the inner mapping group of a loop. We recall some earlier results and by using connected transversals we transform the problem into a group theoretical one. We will get some new answers as we show that a nilpotent group having either $C_\{p^k\} \times C_\{p^l\}$, $k > l \ge 0$ as the Sylow $p$-subgroup for some odd prime $p$ or the group of quaternions as the Sylow $2$-subgroup may not be loop capable.},
author = {Rytty, Miikka},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {loop; group; connected transversals; finite loops; finite nilpotent groups; inner mapping groups; inner automorphism groups; connected transversals},
language = {eng},
number = {2},
pages = {349-355},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On the structure of finite loop capable nilpotent groups},
url = {http://eudml.org/doc/37765},
volume = {51},
year = {2010},
}

TY - JOUR
AU - Rytty, Miikka
TI - On the structure of finite loop capable nilpotent groups
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2010
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 51
IS - 2
SP - 349
EP - 355
AB - In this paper we consider finite loops and discuss the problem which nilpotent groups are isomorphic to the inner mapping group of a loop. We recall some earlier results and by using connected transversals we transform the problem into a group theoretical one. We will get some new answers as we show that a nilpotent group having either $C_{p^k} \times C_{p^l}$, $k > l \ge 0$ as the Sylow $p$-subgroup for some odd prime $p$ or the group of quaternions as the Sylow $2$-subgroup may not be loop capable.
LA - eng
KW - loop; group; connected transversals; finite loops; finite nilpotent groups; inner mapping groups; inner automorphism groups; connected transversals
UR - http://eudml.org/doc/37765
ER -

References

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  9. Mazur M., 10.1515/JGT.2007.015, J. Group Theory 10 (2007), 195–203. Zbl1150.20010MR2302614DOI10.1515/JGT.2007.015
  10. Niemenmaa M., 10.1017/S0004972700038491, Bull. Austral. Math. Soc. 71 (2005), 487–492. Zbl1080.20061MR2150938DOI10.1017/S0004972700038491
  11. Niemenmaa M., On the structure of finite loop capable Abelian groups, Comment. Math. Univ. Carolin. 48,2 (2007), 217–224. Zbl1174.20345MR2338090
  12. Niemenmaa M., 10.1017/S0004972708001093, Bull. Aust. Math. Soc. 79 (2009), 109–114. Zbl1167.20039MR2486887DOI10.1017/S0004972708001093

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