Theorem Let A,B,C be subgroups of G. Let B≤A≤G and C≤G, then we have:
A) A∩BC=B(A∪C) as sets.
B) if B⊴A then B∩C⊴A∩C and (A∩C)/(B∩C)≃B(A∩C)/B
C) If B⊴A and C⊴G then BC⊴AC and AC/BC≃A/B(A∩C).
proof hint: Use Noethers isomorphism theorems and sometimes consider elements.
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