  Linear second order recursive sequences with arbitrary initial conditions
  are studied. For sequences with the same parameters a ring and a group
  is attached, and isomorphisms and homomorphisms are established
  for related parameters. In the group, called the {\it sequence group},
  sequences are identified if they differ by a scalar factor,
  but not if they differ by a shift, which is the case for the Laxton group.
  Prime divisors of sequences are studied with the help of the sequence group
$\mod p$,
  which is always cyclic of order $p\pm 1$.
  Even and odd numbered subsequences are given independent status through
  the introduction of one rational parameter in place of two integer
  parameters. This step brings significant simplifications in the
  algebra.
  All elements of finite order in Laxton groups and sequence
  groups are described effectively.
  A necessary condition is established for a prime $p$
  to be a divisor of a sequence: {\it the norm (determinant) of
  the respective element of the ring must be a quadratic residue $\mod p$}.
  This leads to an uppers estimate of the set of divisors
  by a set of prime density $1/2$. Numerical experiments show that
  the actual density is typically close to $0.35$.
  A conjecture is formulated that the sets of prime divisors of the
  even and odd numbered elements are independent for a large family
  of parameters.
