Spiral arm classifications were made for 261 low-inclination galaxies in groups listed by Huchra and Geller. The fractional occurrence of grand design spiral structure in nonbarred galaxies was found to increase from approx.0.1 to approx.0.6 and then level off as the group crossing rate or galaxy collision rate in a group increases. A simple model is discussed where the random encounters between galaxies of any type and flocculent galaxies induce transient grand design spirals in the flocculent galaxies. If this grand-design stimulation occurs for binary collisions with impact parameters less than ..cap alpha..R/sub 25/, were R/sub 25/ is the galactic radius at 25 mag arcsec/sup -2/, and if the induced grand design spirals persist for an average time equal to ..beta.. galactic rotations, then the quantity ..cap alpha../sup 2/..beta.. equals approximately 3 x 10/sup 4/. If binary collisions are responsible for grand design spirals, then this result implies either that the induced spirals last for many galactic rotations (..beta..>15), or that they can be stimulated by very remote encounters (..cap alpha..>45.) Alternatively, grand design spirals may be stimulated by multiple galaxy encounters, which would be the case for such large ..cap alpha.., or by interactions with the potential well ofmore » the associated group, rather than by simple binary encounters. Weak correlations between the grand design fraction and the galaxy size, or between this fraction and the total number of galaxies in a group, were also found. Spiral structures of barred galaxies show no correlations with group environment.« less