<s>
In	O
mathematics	O
,	O
especially	O
in	O
areas	O
of	O
abstract	O
algebra	O
and	O
finite	O
geometry	O
,	O
the	O
list	B-Algorithm
of	I-Algorithm
transitive	I-Algorithm
finite	I-Algorithm
linear	I-Algorithm
groups	I-Algorithm
is	O
an	O
important	O
classification	O
of	O
certain	O
highly	O
symmetric	O
actions	O
of	O
finite	O
groups	O
on	O
vector	O
spaces	O
.	O
</s>
<s>
The	O
solvable	O
finite	O
2-transitive	B-Algorithm
groups	I-Algorithm
were	O
classified	O
by	O
Bertram	O
Huppert	O
.	O
</s>
<s>
The	O
classification	O
of	O
finite	O
simple	O
groups	O
made	O
possible	O
the	O
complete	O
classification	O
of	O
finite	O
doubly	B-Algorithm
transitive	I-Algorithm
permutation	I-Algorithm
groups	I-Algorithm
.	O
</s>
<s>
A	O
finite	O
2-transitive	B-Algorithm
group	I-Algorithm
has	O
a	O
socle	O
that	O
is	O
either	O
a	O
vector	O
space	O
over	O
a	O
finite	O
field	O
or	O
a	O
non-abelian	O
primitive	O
simple	O
group	O
;	O
groups	O
of	O
the	O
latter	O
kind	O
are	O
almost	O
simple	O
groups	O
and	O
described	O
elsewhere	O
.	O
</s>
<s>
This	O
article	O
provides	O
a	O
complete	O
list	O
of	O
the	O
finite	O
2-transitive	B-Algorithm
groups	I-Algorithm
whose	O
socle	O
is	O
elementary	O
abelian	O
.	O
</s>
<s>
Hence	O
,	O
it	O
has	O
a	O
natural	O
representation	B-Algorithm
as	O
a	O
subgroup	O
of	O
the	O
7-dimensional	O
orthogonal	O
group	O
O(7,q )	O
.	O
</s>
<s>
All	O
but	O
one	O
of	O
the	O
sporadic	O
transitive	O
linear	O
groups	O
yield	O
a	O
primitive	O
permutation	B-Algorithm
group	I-Algorithm
of	O
degree	O
at	O
most	O
2499	O
.	O
</s>
<s>
In	O
the	O
computer	O
algebra	O
programs	O
GAP	B-General_Concept
and	O
MAGMA	B-General_Concept
,	O
these	O
groups	O
can	O
be	O
accessed	O
with	O
the	O
command	O
PrimitiveGroup( p^d	O
,	O
k	O
)	O
;	O
where	O
the	O
number	O
k	O
is	O
the	O
primitive	O
identification	O
of	O
.	O
</s>
