Fitting heights of solvable groups with no nontrivial prime power character degrees
classification
🧮 math.GR
keywords
groupsconstructcharacterfittingheightsonlypowerprime
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We construct solvable groups where the only degree of an irreducible character that is a prime power is $1$ and that have arbitrarily large Fitting heights. We will show that we can construct such groups that also have a Sylow tower. We also will show that we can construct such groups using only three primes.
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