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what even are these symbols?

Source: 2023 Olympic Revenge problem 6

March 28, 2023

group theoryrandomalgebra

Problem Statement

We say that

H

permeates

G

if

G

and

H

are finite groups and for all subgroup

F

of

G

there is

H'\cong H

with

H'\le F

or

F\le H'\le G

. Suppose that a non-abelian group

H

permeates

G

and let

S=\langle H'\le G | H'\cong H\rangle

. Show that

|\bigcap_{H'\in S} H'|>1

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