Geodesic
On the Vanishing of a (G, σ) Product in a (G, σ) Space
Canadian journal of mathematics, Tome 22 (1970) no. 2, pp. 363-371

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In this paper, we shall construct a vector space, called the (G, σ) space, which generalizes the tensor space, the Grassman space, and the symmetric space. Then we shall determine a necessary and sufficient condition that the (G, σ) product of the vectors x 1, x 2, ..., xn is zero. 1. Let G be a permutation group on I = {1, 2, ..., n} and F, an arbitrary field. Let σ be a linear character of G, i.e., σ is a homomorphism of G into the multiplicative group F * of F.For each i ∈ I, let Vi be a finite-dimensional vector space over F. Consider the Cartesian product W = V 1 × V 2 × ... × Vn .1.1. Definition. W is called a G-set if and only if Vi = Vg(i) for all i ∊ I, and for all g ∊ G. 
Singh, K. On the Vanishing of a (G, σ) Product in a (G, σ) Space. Canadian journal of mathematics, Tome 22 (1970) no. 2, pp. 363-371. doi: 10.4153/CJM-1970-044-4
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