Show that L is not isomorphic to (L/K) x K

[alpine quail]

I'm doing an intro group theory course right now and I'm kind of lost on the last portion of this question. I assume you are supposed to mention a specific group like the symmetric group but I'm not sure which examples would work. Also I don't understand the wording of the hint.

[south lagoon]

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[smoky scaffold]

Try finding for example a group that is not abelian with a normal subgroup and it’s quotient group being both abelian

@alpine quail

[alpine quail]

Would it be enough to say that (K/L) x K being abelian but not L shows its true?

[smoky scaffold]

Yeah because if two groups are isomorphic one is abelian if and only if the other is

[alpine quail]

Alright i think i got it then

+close

[lime canyon]

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