## Algebra & Number Theory

### On Oliver's $p$-group conjecture

#### Abstract

Let $S$ be a $p$-group for an odd prime $p$. B. Oliver conjectures that a certain characteristic subgroup $X(S)$ always contains the Thompson subgroup $J(S)$. We obtain a reformulation of the conjecture as a statement about modular representations of $p$-groups. Using this we verify Oliver’s conjecture for groups where $S∕X(S)$ has nilpotence class at most two.

#### Article information

Source
Algebra Number Theory, Volume 2, Number 8 (2008), 969-977.

Dates
Revised: 14 August 2008
Accepted: 19 September 2008
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.ant/1513805231

Digital Object Identifier
doi:10.2140/ant.2008.2.969

Mathematical Reviews number (MathSciNet)
MR2457358

Zentralblatt MATH identifier
1173.20015

Subjects
Primary: 20D15: Nilpotent groups, $p$-groups

#### Citation

Green, David; Héthelyi, László; Lilienthal, Markus. On Oliver's $p$-group conjecture. Algebra Number Theory 2 (2008), no. 8, 969--977. doi:10.2140/ant.2008.2.969. https://projecteuclid.org/euclid.ant/1513805231

#### References

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