n is an odd composite number, with n-1 = t* 2^s where t is odd

Define S(n) := { 0<= a <= n-1 | n is a strong psuedoprime base a}

T(n):= { 0<= a <= n-1 | a^(t*2^(v-1)) = +1 or -1 (mod n)}

where v above is the largest integer such that 2^v divides p-1 for all prime factors p of n }

How can I show that T(n) is a subgroup of the group of units of Z_n and is generated by S(n)?