Let $\mathcal{S}_q$ denote the group of all square elements in the multiplicative group $\mathbb{F}_q^*$ of a finite field $\mathbb{F}_q$ of odd characteristic containing $q$ elements. Let $\mathcal{O}_q$ be the set of all odd order elements of $\mathbb{F}_q^*$. Then $\mathcal{O}_q$ turns up as a subgroup of $\mathcal{S}_q$. In this paper, we show that $\mathcal{O}_q=\langle4\rangle$ if $q=2t+1$ and, $\mathcal{O}_q=\langle t\rangle $ if $q=4t+1$, where $q$ and $t$ are odd primes. Further, we determine the coefficients of irreducible factors of $x^{2^nt}-1$ using generators of these special subgroups of $\mathbb{F}_q^*$
Singh, M. (2019). Some subgroups of $\mathbb{F}_q^*$ and explicit factors of $x^{2^nd}-1\in\mathbb{F}_q[x]$. Transactions on Combinatorics, 8(4), 23-33. doi: 10.22108/toc.2019.114742.1612
MLA
Manjit Singh. "Some subgroups of $\mathbb{F}_q^*$ and explicit factors of $x^{2^nd}-1\in\mathbb{F}_q[x]$". Transactions on Combinatorics, 8, 4, 2019, 23-33. doi: 10.22108/toc.2019.114742.1612
HARVARD
Singh, M. (2019). 'Some subgroups of $\mathbb{F}_q^*$ and explicit factors of $x^{2^nd}-1\in\mathbb{F}_q[x]$', Transactions on Combinatorics, 8(4), pp. 23-33. doi: 10.22108/toc.2019.114742.1612
VANCOUVER
Singh, M. Some subgroups of $\mathbb{F}_q^*$ and explicit factors of $x^{2^nd}-1\in\mathbb{F}_q[x]$. Transactions on Combinatorics, 2019; 8(4): 23-33. doi: 10.22108/toc.2019.114742.1612
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