CLASS-PRESERVING AUTOMORPHISMS OF A FAMILY OF FINITE p-GROUPS
نویسنده
چکیده
Let G be a finite p-group, p prime such that G has a normal subgroup H , there exists an element y ∈ G, y / ∈ H such that order of y is p, y ∈ ζ(G) and each element g ∈ G can be written as g = h y, h ∈ H, 1 ≤ i ≤ p, where ζ(G) denotes the center of G. It is proved that any τ ∈ Autc(G) such that for all x ∈ H , xτ = (uy)x(uy), where u is a fixed element of H and 1 ≤ i ≤ p is an inner automorphism of G. As a consequence it is proved that Outc(G) = 1, where G is a finite p-group of order p , p an odd prime.
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