# Revision history [back]

You should tell us how you construct B. As for me, it works as expected:

sage: G = SL(2,GF(3)) ; G
Special Linear Group of degree 2 over Finite Field of size 3
sage: a = G.gens()[0] ; a
[1 1]
[0 1]
sage: G.subgroup([a])
Matrix group over Finite Field of size 3 with 1 generators (
[1 1]
[0 1]
)


You should tell us how you construct B. As for me, it works as expected:

sage: G = SL(2,GF(3)) ; G
Special Linear Group of degree 2 over Finite Field of size 3
sage: a = G.gens()[0] ; a
[1 1]
[0 1]
sage: G.subgroup([a])
H = G.subgroup([a]) ; H
Matrix group over Finite Field of size 3 with 1 generators (
[1 1]
[0 1]
)
sage: a^2 in H
True


You should tell us how you construct B. is constructed. As for me, it works as expected:

sage: G = SL(2,GF(3)) ; G
Special Linear Group of degree 2 over Finite Field of size 3
sage: a = G.gens()[0] ; a
[1 1]
[0 1]
sage: H = G.subgroup([a]) ; H
Matrix group over Finite Field of size 3 with 1 generators (
[1 1]
[0 1]
)
sage: a^2 in H
True


You should tell us how B is constructed. As for me, it works as expected:

sage: G = SL(2,GF(3)) ; G
Special Linear Group of degree 2 over Finite Field of size 3
sage: a = G.gens()[0] ; a
[1 1]
[0 1]
sage: H = G.subgroup([a]) ; H
Matrix group over Finite Field of size 3 with 1 generators (
[1 1]
[0 1]
)
sage: a^2 in H
True
sage: G.gens()[1]
[0 1]
[2 0]
sage: G.gens()[1] in H
False


You should tell us how B is constructed. constructed, otherwise we will not be able to understand where is your problem coming from. As for me, it works as expected:

sage: G = SL(2,GF(3)) ; G
Special Linear Group of degree 2 over Finite Field of size 3
sage: a = G.gens()[0] ; a
[1 1]
[0 1]
sage: H = G.subgroup([a]) ; H
Matrix group over Finite Field of size 3 with 1 generators (
[1 1]
[0 1]
)
sage: a^2 in H
True
sage: G.gens()[1]
[0 1]
[2 0]
sage: G.gens()[1] in H
False