Permutation Representations and Group Actions

There are fairly general examples due to Conlon in the paper:

Conlon, S.B., Monomial representations under integral similarity, J. Algebra 13, 496-508 (1969). ZBL0185.06702.

There is even a transitive example, due to Scott:

Scott, Leonard L., Integral equivalence of permutation representations, Sehgal, Surinder (ed.) et al., Group theory. Proceedings of the 21st biennial Ohio State-Denison mathematical conference, Granville, OH (USA), 14-16 May, 1992. Singapore: World Scientific. 262-274 (1993). ZBL0828.20004.

In this example, $G$ is $\text{PSL}(2,29)$ and the permutation actions are on the cosets of two non-conjugate subgroups both isomorphic to the alternating group $A_5$.

Tags:

Permutations

Abstract Algebra

Group Theory

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