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Part BCSIR NET June 2024hom-count-is-the-gcd

Hom count is the gcd

The number of group homomorphisms from Z/150Z\mathbb{Z}/150\mathbb{Z} to Z/90Z\mathbb{Z}/90\mathbb{Z} is

  1. A.30✓ Correct
  2. B.60
  3. C.45
  4. D.10

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward, and why this one tests standard counterexample.

See pricing

50 are analysed free — try those first.

The trap it tests

Standard counterexample

There is a canonical object that settles this. Recognising it is the whole question.

Drill statements like this

Related counterexample: If d divides |G| then G has a subgroup of order d

More on this topic

The chapter behind this: Lagrange, orders and cyclic groups — free to read

From Groups › Subgroups, cosets, Lagrange, cyclic groups

Last revised . Found a mistake? Tell us — corrections are the fastest thing we act on.

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