TY - JOUR

T1 - On Oliver's p-group conjecture :

T2 - II.

AU - Green, David

AU - Héthelyi, László

AU - Mazza, Nadia

PY - 2010/5

Y1 - 2010/5

N2 - Let $p$ be an odd prime and $S$ a finite $p$-group. B.~Oliver's conjecture arises from an open problem in the theory of $p$-local finite groups and says that a certain characteristic subgroup $\mathfrak{X}(S)$ of $S$ always contains the Thompson subgroup. In previous work the first two authors and M.~Lilienthal recast Oliver's conjecture as a statement about the representation theory of the factor group $S/\mathfrak{X}(S)$. We now verify the conjecture for a wide variety of groups~$S/\mathfrak{X}(S)$.

AB - Let $p$ be an odd prime and $S$ a finite $p$-group. B.~Oliver's conjecture arises from an open problem in the theory of $p$-local finite groups and says that a certain characteristic subgroup $\mathfrak{X}(S)$ of $S$ always contains the Thompson subgroup. In previous work the first two authors and M.~Lilienthal recast Oliver's conjecture as a statement about the representation theory of the factor group $S/\mathfrak{X}(S)$. We now verify the conjecture for a wide variety of groups~$S/\mathfrak{X}(S)$.

U2 - 10.1007/s00208-009-0435-4

DO - 10.1007/s00208-009-0435-4

M3 - Journal article

VL - 347

SP - 111

EP - 122

JO - Mathematische Annalen

JF - Mathematische Annalen

SN - 0025-5831

IS - 1

ER -