<s>
In	O
mathematics	O
,	O
a	O
Gassmann	B-Algorithm
triple	I-Algorithm
(	O
or	O
Gassmann-Sunada	O
triple	O
)	O
is	O
a	O
group	O
G	O
together	O
with	O
two	O
faithful	O
actions	O
on	O
sets	O
X	O
and	O
Y	O
,	O
such	O
that	O
X	O
and	O
Y	O
are	O
not	O
isomorphic	O
as	O
G-sets	O
but	O
every	O
element	O
of	O
G	O
has	O
the	O
same	O
number	O
of	O
fixed	O
points	O
on	O
X	O
and	O
Y	O
.	O
</s>
<s>
Gassmann	B-Algorithm
triples	I-Algorithm
have	O
been	O
used	O
to	O
construct	O
examples	O
of	O
pairs	O
of	O
mathematical	O
objects	O
with	O
the	O
same	O
invariants	O
that	O
are	O
not	O
isomorphic	O
,	O
including	O
arithmetically	O
equivalent	O
number	O
fields	O
and	O
isospectral	O
graphs	O
and	O
isospectral	O
Riemannian	O
manifolds	O
.	O
</s>
<s>
The	O
simple	O
group	O
G	O
=	O
SL3(F2 )	O
of	O
order	O
168	O
acts	O
on	O
the	O
projective	O
plane	O
of	O
order	O
2	O
,	O
and	O
the	O
actions	O
on	O
the	O
7	O
points	O
and	O
7	O
lines	O
give	O
a	O
Gassmann	B-Algorithm
triple	I-Algorithm
.	O
</s>
