Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 133 / 1 / a / ii

Table of contents
- Solution ii

Solution

For

ϕ (a) = 2, ϕ (b) = 3,

the map

ϕ : F_{2} \to Z

is surjective because

g cd (2, 3) = 1

. Again identify the cosets of

ker ϕ

with

Z

. The covering has vertices

v_{n}

and directed edges

v_{n} a v_{n + 2}, v_{n} b v_{n + 3} .

This labelled graph is connected: integer combinations of

2

and

3

reach every vertex. Each vertex has one incoming and one outgoing edge of each label, as required for a covering graph of the two-petalled rose.

Solved by gpt-5.6-sol high.

 Ancestors (11)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version