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6

Part of 2023 Olympic Revenge

Problems(1)

what even are these symbols?

Source: 2023 Olympic Revenge problem 6

3/28/2023
We say that HH permeates GG if GG and HH are finite groups and for all subgroup FF of GG there is H′≅HH'\cong H with H′≤FH'\le F or F≤H′≤GF\le H'\le G. Suppose that a non-abelian group HH permeates GG and let S=⟨H′≤G∣H′≅H⟩S=\langle H'\le G | H'\cong H\rangle. Show that ∣⋂H′∈SH′∣>1|\bigcap_{H'\in S} H'|>1
group theoryrandomalgebra