TY - JOUR
T1 - Finite p-groups with normal normalisers
AU - Ormerod, Elizabeth A.
AU - Parmeggiani, Gemma
PY - 2004/2
Y1 - 2004/2
N2 - We consider the class N of groups in which the normaliser of every subgroup is normal, and the class C of groups in which the commutator subgroup normalises every subgroup. It is clear that C ⊆ N, and it is known that groups in the class N are nilpotent of class at most 3. We show that every finite p-group in N is also in C, provided that p ≥ 5, and we give an example showing that this is not true for p = 2.
AB - We consider the class N of groups in which the normaliser of every subgroup is normal, and the class C of groups in which the commutator subgroup normalises every subgroup. It is clear that C ⊆ N, and it is known that groups in the class N are nilpotent of class at most 3. We show that every finite p-group in N is also in C, provided that p ≥ 5, and we give an example showing that this is not true for p = 2.
UR - http://www.scopus.com/inward/record.url?scp=1842592773&partnerID=8YFLogxK
U2 - 10.1017/s0004972700034341
DO - 10.1017/s0004972700034341
M3 - Article
SN - 0004-9727
VL - 69
SP - 141
EP - 150
JO - Bulletin of the Australian Mathematical Society
JF - Bulletin of the Australian Mathematical Society
IS - 1
ER -