Fitting heights of solvable groups with no nontrivial prime power character degrees
Abstract
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- June 2015
- DOI:
- 10.48550/arXiv.1506.07148
- arXiv:
- arXiv:1506.07148
- Bibcode:
- 2015arXiv150607148L
- Keywords:
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- Mathematics - Group Theory;
- 20C15;
- 20D10
- E-Print:
- 6 pages