Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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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 -