## Osaka Journal of Mathematics

### Reduction theorems for characteristic functors on finite $p$-groups and applications to $p$-nilpotence criteria

Paul Lescot

#### Abstract

We formalize various properties of characteristic functors on $p$-groups, and discuss relationships between them. Applications to the Thompson subgroup and certain of its analogues are then given.

#### Article information

Source
Osaka J. Math., Volume 45, Number 4 (2008), 1043-1056.

Dates
First available in Project Euclid: 26 November 2008

https://projecteuclid.org/euclid.ojm/1227708832

Mathematical Reviews number (MathSciNet)
MR2493969

Zentralblatt MATH identifier
1170.20011

Subjects
Primary: 20D20: Sylow subgroups, Sylow properties, $\pi$-groups, $\pi$-structure
Secondary: 20E25: Local properties

#### Citation

Lescot, Paul. Reduction theorems for characteristic functors on finite $p$-groups and applications to $p$-nilpotence criteria. Osaka J. Math. 45 (2008), no. 4, 1043--1056. https://projecteuclid.org/euclid.ojm/1227708832

#### References

• S.F. Bauman: Groups with $p$-length $1$, J. Algebra 8 (1968), 388--392.
• G. Glauberman: A characteristic subgroup of a $p$-stable group, Canad. J. Math. 20 (1968), 1101--1135.
• G. Glauberman: Factorizations in Local Subgroups of Finite Groups, Regional Conference Series in Mathematics 33, Amer. Math. Soc., Providence, R.I., 1977.
• D. Gorenstein: Finite Simple Groups, Plenum, New York, 1982.
• M. Hayashi: $2$-factorization in finite groups, Pacific J. Math. 84 (1979), 97--142.
• P. Lescot: Sur la factorisation de Thompson, Revue de Mathématiques Spéciales 99 (1989), 197--198.
• B. Stellmacher: A characteristic subgroup of $\Sigma\sb 4$-free groups, Israel J. Math. 94 (1996), 367--379.
• J.G. Thompson: Normal $p$-complements for finite groups, J. Algebra 1 (1964), 43--46.
• J.G. Thompson: Factorizations of $p$-solvable groups, Pacific J. Math. 16 (1966), 371--372.