
Alexander Ivanov
Imperial College
Triextraspecial groups
Friday 26th March, 12:0512:55pm,
Carslaw 373.
The talk is based on a joint work with Sergey V. Shpectorov
on a class of groups, which are certain split
extensions of special 2groups 2^{3+6n}
by L_{3}(2). We
call these groups triextraspecial, because they behave very much like
extraspecial 2groups. For every value of n, there are exactly two
such groups, denoted T^{±}(n).
We show that the outer automorphism group of
T^{±}(n) is 2 x Sp(2n,2).
The group Out(T^{±}(n)) acts transitively on
the classes of complements L_{3}(2) in
T^{±}(n), the stabilizer of
such a class being O^{±}(2n,2). The group
T^{±}(n) arises as a
normal subgroup in a maximal parabolic subgroup (the stabilizer of a
3dimensional totally singular subspace) of
O^{±}(2n+6,2). Even
more remarkably, the groups T^{+}(4) and T^{}(4) arise,
respectively, in the sporadic groups J_{4} and
F_{24}.
These latter examples were
the primary motivation of our interest in triextraspecial groups.







