## On the heights of group characters

HTML articles powered by AMS MathViewer

- by R. J. Haggarty
- Proc. Amer. Math. Soc.
**63**(1977), 213-216 - DOI: https://doi.org/10.1090/S0002-9939-1977-0435199-1
- PDF | Request permission

## Abstract:

For a finite*p*-soluble group

*G*we derive a bound on the heights of the irreducible complex characters of

*G*lying in a

*p*-block

*B*. This bound depends on the prime

*p*and the exponent

*d*of a defect group of

*B*. We show by examples that this bound is of the right order of magnitude.

## References

- Richard Brauer,
*Some applications of the theory of blocks of characters of finite groups. IV*, J. Algebra**17**(1971), 489–521. MR**281806**, DOI 10.1016/0021-8693(71)90006-8 - Richard Brauer and Walter Feit,
*On the number of irreducible characters of finite groups in a given block*, Proc. Nat. Acad. Sci. U.S.A.**45**(1959), 361–365. MR**106246**, DOI 10.1073/pnas.45.3.361 - Paul Fong,
*Some properties of characters of finite solvable groups*, Bull. Amer. Math. Soc.**66**(1960), 116–117. MR**111794**, DOI 10.1090/S0002-9904-1960-10422-3 - P. Fong,
*On the characters of $p$-solvable groups*, Trans. Amer. Math. Soc.**98**(1961), 263–284. MR**120297**, DOI 10.1090/S0002-9947-1961-0120297-5 - P. Hall and Graham Higman,
*On the $p$-length of $p$-soluble groups and reduction theorems for Burnside’s problem*, Proc. London Math. Soc. (3)**6**(1956), 1–42. MR**72872**, DOI 10.1112/plms/s3-6.1.1 - B. Huppert,
*Endliche Gruppen. I*, Die Grundlehren der mathematischen Wissenschaften, Band 134, Springer-Verlag, Berlin-New York, 1967 (German). MR**0224703**
—, - David L. Winter,
*$p$-solvable linear groups of finite order*, Trans. Amer. Math. Soc.**157**(1971), 155–160. MR**276345**, DOI 10.1090/S0002-9947-1971-0276345-1

*Linear auflösbare Gruppen*, Math. Z.

**67**(1957), 479-518. MR

**19**, 729.

## Bibliographic Information

- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**63**(1977), 213-216 - MSC: Primary 20C20
- DOI: https://doi.org/10.1090/S0002-9939-1977-0435199-1
- MathSciNet review: 0435199