Geodesic
On Quasi-g-Circulant Matrices
Séminaire lotharingien de combinatoire, Tome 13 (1985) 
Norma Zagaglia Salvi. On Quasi-g-Circulant Matrices. Séminaire lotharingien de combinatoire, Tome 13 (1985). http://geodesic.mathdoc.fr/item/SLC_1985_13_a6/
@article{SLC_1985_13_a6,
     author = {Norma Zagaglia Salvi},
     title = {On {Quasi-g-Circulant} {Matrices}},
     journal = {S\'eminaire lotharingien de combinatoire},
     year = {1985},
     volume = {13},
     url = {http://geodesic.mathdoc.fr/item/SLC_1985_13_a6/}
}
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JO  - Séminaire lotharingien de combinatoire
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ID  - SLC_1985_13_a6
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%J Séminaire lotharingien de combinatoire
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Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

A matrix Q of order n is called k-quasi-g-circulant if it satisfies

PkQ = QPkg,

where P represents the permutation (1 2 ... n), (n,g)=1, and the exponents are mod n.

We prove that if (k,n)=h, a matrix Q is k-quasi-g-circulant if and only if it is h-quasi-g-circulant; then Q is a block g-circulant matrix of type (q,h), and we give a characterization for these matrices. Moreover, we define a perfect k-quasi-g-circulant permutation, and we prove that the set of these permutations is an imprimitive group of order φ(k)kqk, where φ(k) is the Euler function of k, that is the number of positive integers not greater than and prime to k.

The main part of the results of this paper have appeared in the article "On the solutions of a matrix equation," Boll. Un. Mat. Ital. 3-A (1989), 137-145.