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Results tagged with symmetric-groups
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user 516285
The symmetric group $S_n$ is the group of permutations of the set of integers $\{1,\dots,n\}$. This has $n!$ elements and is generated by the $n-1$ involutions exchanging consecutive integers. The symmetric groups form the simplest family of Coxeter groups.
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Invertibility of one matrix constructed by order n subgroup of symmetric group
The answer is no. Consider the subgroup generated by (1243). The matrix you have will be cyclic. See Determinant of cyclic matrix, proof without eigenvectors for a discussion of the determinant.
It is …
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