Permutability of centre-by-finite groups

Brunetto Piochi

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti (1989)

  • Volume: 83, Issue: 1, page 153-158
  • ISSN: 0392-7881

Abstract

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Let G be a group and m be an integer greater than or equal to 2 . G is said to be m -permutable if every product of m elements can be reordered at least in one way. We prove that, if G has a centre of finite index z , then G is ( 1 + [ z / 2 ] ) -permutable. More bounds are given on the least m such that G is m -permutable.

How to cite

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Piochi, Brunetto. "Permutability of centre-by-finite groups." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti 83.1 (1989): 153-158. <http://eudml.org/doc/289079>.

@article{Piochi1989,
abstract = {Let $G$ be a group and $m$ be an integer greater than or equal to $2$. $G$ is said to be $m$-permutable if every product of $m$ elements can be reordered at least in one way. We prove that, if $G$ has a centre of finite index $z$, then $G$ is $(1 + [z/2])$-permutable. More bounds are given on the least $m$ such that $G$ is $m$-permutable.},
author = {Piochi, Brunetto},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
keywords = {Centre-by-Finite Groups; Rewritable groups; Permutability},
language = {eng},
month = {12},
number = {1},
pages = {153-158},
publisher = {Accademia Nazionale dei Lincei},
title = {Permutability of centre-by-finite groups},
url = {http://eudml.org/doc/289079},
volume = {83},
year = {1989},
}

TY - JOUR
AU - Piochi, Brunetto
TI - Permutability of centre-by-finite groups
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
DA - 1989/12//
PB - Accademia Nazionale dei Lincei
VL - 83
IS - 1
SP - 153
EP - 158
AB - Let $G$ be a group and $m$ be an integer greater than or equal to $2$. $G$ is said to be $m$-permutable if every product of $m$ elements can be reordered at least in one way. We prove that, if $G$ has a centre of finite index $z$, then $G$ is $(1 + [z/2])$-permutable. More bounds are given on the least $m$ such that $G$ is $m$-permutable.
LA - eng
KW - Centre-by-Finite Groups; Rewritable groups; Permutability
UR - http://eudml.org/doc/289079
ER -

References

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  1. CURZIO, M., 1985. Sul problema di Burnside. Quad. Ist. Mat. Appi. Univ. L'Aquila, 8: 1-24. 
  2. CURZIO, M., LONGOBARDI, P. and MAJ, M., 1983. Su di un problema combinatorio in Teoria dei Gruppi. Atti Acc. Lincei Rend. fis., VIII, 74: 136-142. Zbl0528.20031
  3. CURZIO, M., LONGOBARDI, P., MAY, M. and ROBINSON, D.J.S., 1985. A permutational property of groups. Arch. Math., 44: 385-389. Zbl0544.20036MR792360DOI10.1007/BF01229319
  4. GARZON, M. and ZALCSTEIN, Y., 1987. On permutation properties in groups and semigroups. Semigroup Forum, 35: 337-351. Zbl0623.20040MR900108DOI10.1007/BF02573115
  5. PIOCHI, B. and PIRILLO, G., 1988. Sur une propriété combinatone des groupes finis. C.R. Acad. Sci. Paris, 307, I: 115-117. Zbl0647.20032MR954272
  6. RESTTVO, A. and REUTENAUER, C., 1984. On the Burnside problem for semigroups. J. Algebra, 89; 102-104. Zbl0545.20051MR748230DOI10.1016/0021-8693(84)90237-0
  7. SUZUKI, M., 1982. Group Theory I. Springer Verlag, Berlin. MR648772

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