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In this paper, we study distance one surgeries between lens spaces  L(p, 1)  with  p  ≥ 5 prime and lens spaces  L(n, 1)  for$$n \in \mathbb{Z}$$    and band surgeries from  T (2, p)  to  T (2, n) . In particular, we prove that  L(n, 1)  is obtained by a distance one surgery from  L(5, 1)  only if  n =±1, 4, ±5, 6 or ±9, and  L(n, 1)  is obtained by a distance one surgery from  L(7, 1)  if and only if  n =±1, 3, 6, 7, 8 or 11.

Studies of distance one surgeries on the lens space L(p, 1)