Algebra & Number Theory

On Oliver's $p$-group conjecture

David Green, László Héthelyi, and Markus Lilienthal

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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 SX(S) has nilpotence class at most two.

Article information

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

Received: 17 April 2008
Revised: 14 August 2008
Accepted: 19 September 2008
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

$p$-group characteristic subgroup Thompson subgroup $p$-local finite group Replacement Theorem


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.

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