A characterization of saturated fusion systems over abelian 2-groups
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A characterization of saturated fusion systems over abelian 2-groups. / Henke, Ellen.
I: Advances in Mathematics, Bind 127, 2014, s. 1-5.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - A characterization of saturated fusion systems over abelian 2-groups
AU - Henke, Ellen
PY - 2014
Y1 - 2014
N2 - Given a saturated fusion system FF over a 2-group S, we prove that S is abelian provided any element of S is F-conjugate to an element of Z(S). This generalizes a Theorem of Camina–Herzog, leading to a significant simplification of its proof. More importantly, it follows that any 2-block B of a finite group has abelian defect groups if all B-subsections are major. Furthermore, every 2-block with a symmetric stable center has abelian defect groups.
AB - Given a saturated fusion system FF over a 2-group S, we prove that S is abelian provided any element of S is F-conjugate to an element of Z(S). This generalizes a Theorem of Camina–Herzog, leading to a significant simplification of its proof. More importantly, it follows that any 2-block B of a finite group has abelian defect groups if all B-subsections are major. Furthermore, every 2-block with a symmetric stable center has abelian defect groups.
U2 - 10.1016/j.aim.2014.02.020
DO - 10.1016/j.aim.2014.02.020
M3 - Journal article
VL - 127
SP - 1
EP - 5
JO - Advances in Mathematics
JF - Advances in Mathematics
SN - 0001-8708
ER -
ID: 137755021