  It is known that for $\sigma$-compact groups Kazhdan's Property $(T)$ is
equivalent to Serre's Property $(FH)$. Generalized versions of those
properties, called properties $(T_{B})$ and $(F_{B})$, can be defined in terms
of the isometric representations of a group on an arbitrary Banach space $B$.
Property $(F_{B})$ implies $(T_{B})$. It is known that a group with Property
$(T_{l_p})$ shares some properties with Kazhdan's groups, for example compact
generation and compact abelianization. Moreover in the case of discrete groups,
Property $(T_{l_p})$ implies Lubotzky's Property $(\tau)$. In this paper we
prove that in the case of discrete groups and $1<p<q<\infty$ and $p\not=2$,
Property $(F_{l_q})$ implies Property $(F_{l_p})$.
