Abstract
Given a finite group G, we say that G has property \(\mathcal P_{k}\) if every set of k distinct irreducible character degrees of G is setwise relatively prime. In this paper, we show that if G is a finite nonsolvable group satisfying \(\mathcal P_{4}, \)then G has at most 8 distinct character degrees. Combining with work of D. Benjamin on finite solvable groups, we deduce that a finite group G has at most 9 distinct character degrees if G has property \(\mathcal P_{4}\) and this bound is sharp.
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Presented by Radha Kessar.
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Ghaffarzadeh, M., Ghasemi, M., Lewis, M.L. et al. Nonsolvable Groups with no Prime Dividing Four Character Degrees. Algebr Represent Theor 20, 547–567 (2017). https://doi.org/10.1007/s10468-016-9654-z
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DOI: https://doi.org/10.1007/s10468-016-9654-z