fintype (sylow p G)

Stream: maths

[Joachim Breitner]

If I have a subgroup H < G, should I expect that fintype (sylow p G) implies fintype (sylow p H)?
If yes, I could weaken the assumptions of some of my lemmas.

[Thomas Browning]

Actually, I think so: For every Sylow subgroup P of H, take a Sylow subgroup Q of G containing it. Then P is the intersection of Q with H.

[Thomas Browning]

So there is an injective function from Sylow subgroups of H to Sylow subgroups of G.

[Joachim Breitner]

Thanks! Maybe I’ll add that later, once my current work is in.

[Thomas Browning]

@Joachim Breitner #11664