  In this letter, the integrability aspects of a generalized Fisher type
equation with modified diffusion in (1+1) and (2+1) dimensions are studied by
carrying out a singularity structure and symmetry analysis. It is shown that
the Painlev\'e property exists only for a special choice of the parameter
($m=2$). A B\"acklund transformation is shown to give rise to the linearizing
transformation to the linear heat equation for this case ($m=2$). A Lie
symmetry analysis also picks out the same case ($m=2$) as the only system among
this class as having nontrivial infinite dimensional Lie algebra of symmetries
and that the similarity variables and similarity reductions lead in a natural
way to the linearizing transformation and physically important classes of
solutions (including known ones in the literature), thereby giving a group
theoretical understanding of the system. For nonintegrable cases in (2+1)
dimensions, associated Lie symmetries and similarity reductions are indicated.
