Abstract
A group G is said to enjoy Hasse principle if every local coboundary of G is a global coboundary. Let G be a non-Abelian finite p-group of order p m , p prime and m > 4 having a normal cyclic subgroup of order p m-2 but having no element of order p m-1 . We prove that G enjoys Hasse principle if p is odd but in the case p = 2, there are fourteen such groups twelve of which enjoy Hasse principle but the remaining two do not satisfy Hasse principle. We also find all the conjugacy preserving outer automorphisms for these two groups.
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