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Constructing solvable groups whose character degree graphs generalize the bowtie
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Constructing solvable groups whose character degree graphs generalize the bowtie

Jacob Laubacher, Mark L Lewis, Lorenzo Ravaglia and Andrew Summers
19/08/2026

Abstract

Mathematics - Combinatorics Mathematics - Group Theory
We present here a generalized construction of a finite solvable group whose prime character degree graph has the shape and structure of the bowtie graph. As with the original bowtie, the graphs obtained by this generalized construction, under certain restrictions, cannot be realized by the usual method of taking direct products of smaller graphs. Within the condition ofn=1 , we show how this recovers the original bowtie graph, which has five vertices. We also provide examples and explicit choices of primes which generate graphs with more vertices.

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