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On Subsequence Weighted Products

Published online by Cambridge University Press:  21 July 2005

Y. O. HAMIDOUNE  and
D. QUIROZ
Y. O. HAMIDOUNE
Affiliation:
Université Pierre et Marie Curie, E. Combinatoire, Case 189, 4 Place Jussieu, 75005 Paris, France (e-mail: yha@ccr.jussieu.fr)
D. QUIROZ
Affiliation:
Universidad Simón Bolívar, Departamento de Matemática, Ap. 89000, Caracas, Venezuela (e-mail: dquiroz@usb.ve)
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Abstract

Let $G$ be a finite group of order $n$ and let $k$ be a natural number. Let $\{x_i : i\in I\}$ be a family of elements of $G$ such that $|I|= n+k-1$. Let $v$ be the most repeated value of the family. Let $ \{ \sigma_i : 1\leq i \leq k \} $ be a family of permutations of $G$ such that $\sigma_i(1)=1$ for all $i$. We obtain the following result.

There are pairwise distinct elements $i_1, i_2, \dots ,i_k\in I$ such that \[ \prod_{1\leq j\leq k } \sigma_j \big(v^{-1}x_ {i_j }\big) =1.\]

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 14 , Issue 4 , July 2005 , pp. 485 - 489
Copyright
© 2005 Cambridge University Press

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