MathCastle
Groups and FieldsChallengeNormal Subgroups and Quotient Groups

Normal Subgroups and Quotient Groups · Challenge problem

A homomorphism φ:G→H\varphi: G \to H has ∣G∣=100|G| = 100 and ∣H∣=15|H| = 15. How many different values could ∣ker⁡φ∣|\ker\varphi| possibly take?