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22 Nov 2022: 1. (i) What are the transitive subgroups of S4? Find a monic polynomial over Z of degree 4 whoseGalois group is V = {e, (12)(34), (13)(24), (14)(23)}.(ii) Let

8 Nov 2021: a) Let H 6 Cn. Identify the quotient Cn/H. (b) Show that N = {e, (12)(34), (13)(24), (14)(23)} is a normal subgroup of S4.

26 Oct 2021: g]| 1 21 42 56 24 24α 14 2 0 1 0 0β 15 1 1 0 1 1γ 16 0 0 2 2 2.

8 Sep 2020: 54. 56. 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 ... 44. 46. 48. 50. 52. 54. 56. 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52

5 Nov 2018: 1) = 1. There must be a 24-path from x2 to x4 or we can make some colour swap and colour v. ... 1) = 1. There must be a 23-path from x2 to x3 and a 24-path from x2 to x4 or we can make some colour swap and.

15 Jan 2024: X4 2X 2, X4 18X2 24, X3 9, X3 X2 X 1, X4 1, X4 4.

12 Jul 2024: V Chulaevsky, AB de Monvel, Y Suhov. – Nonlinearity. (2011). 24,. ... 1451. (doi: 10.1088/0951-7715/24/5/004). An isoperimetric inequality for the Wiener sausage. Y Peres, P Sousi. –

25 Oct 2023: g]| 1 21 42 56 24 24α 14 2 0 1 0 0β 15 1 1 0 1 1γ 16 0 0 2 2 2.

12 Nov 2005: Find a monic polynomial over Z of degree 4 whoseGalois group is V = {e, (12)(34), (13)(24), (14)(23)}.(ii) Let f Z[X] be monic and separable of degree

2 Nov 2019: π2. 3. (1 24. n=1. σ1(n)qn. ). Explain why G2(z) is not a modular form of weight 2.