 
Summary: ILLINOIS JOURNAL OF MATHEMATICS
Volume 24, Number 2, Summer 1980
2COHOMOLOGY OF SOME UNITARY GROUPS
BY
GEORGE S. AVRUNIN
In [1], we showed that the 2cohomology of the group SU(n, q)with
coefficients in the standard module V l is generally zero. For SU(2, q),
which is, of course, equal to SL(2, q2), the only exceptions occur at q 2k
with
k _> 2; in unpublished work, McLaughlin has shown that the second cohom
ology group has dimension 1 over Fq2. For n > 2 and q > 3, the only possible
exceptions are at n 3 with q 4 or 3k
and n 4 with q 4. In this paper, we
prove that H2(SU(n, q), V) has dimension 1 over Fq2 in the first case and
vanishes in the second. We also show that H2(SU(3, 3), V)is zero.
In Section l, we outline some basic results on the cohomology of groups. In
the second section, we compute HE(su(3, q), V) with q 4 or 3k, k > 1, while
the 2cohomology of SU(4, 4) is determined in the third section. Finally, we
show H2(SU(3, 3), V)= 0 in the fourth section.
I. In this section, we describe some results on the cohomology of groups
