Babaei, E., Zamani, Y. (2014). Symmetry classes of polynomials associated with the direct product of permutation groups. International Journal of Group Theory, 3(4), 63-69. doi: 10.22108/ijgt.2014.5479

Esmaeil Babaei; Yousef Zamani. "Symmetry classes of polynomials associated with the direct product of permutation groups". International Journal of Group Theory, 3, 4, 2014, 63-69. doi: 10.22108/ijgt.2014.5479

Babaei, E., Zamani, Y. (2014). 'Symmetry classes of polynomials associated with the direct product of permutation groups', International Journal of Group Theory, 3(4), pp. 63-69. doi: 10.22108/ijgt.2014.5479

Babaei, E., Zamani, Y. Symmetry classes of polynomials associated with the direct product of permutation groups. International Journal of Group Theory, 2014; 3(4): 63-69. doi: 10.22108/ijgt.2014.5479

Symmetry classes of polynomials associated with the direct product of permutation groups

Let $G_{i} $ be a subgroup of $ S_{m_{i}} ,\ 1 \leq i \leq k$. Suppose $\chi_{i}$ is an irreducible complex character of $G_{i}$. We consider $ G_{1}\times \cdots \times G_{k} $ as subgroup of $ S_{m} $, where $ m=m_{1}+\cdots +m_{k} $. In this paper, we give a formula for the dimension of $H_{d}(G_{1}\times \cdots \times G_{k}, \chi_{1}\times\cdots \times \chi_{k})$ and investigate the existence of an o-basis of this type of classes.

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