Let G be a finite two generated p-group of nilpotency class two, where p is a prime number. If ф(G) is the Frattini subgroup of G, then G/ ф(G) is a vector space of dimension two over the field. In this paper, we determine those automorphisms on G which induce identity transformation on G/ф(G). We use the most updated classification given for G to find these automorphisms. The results of this study are applicable in classifying (G), theautomorphism group of G.
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