Tutorial Sheet 3: Algebraic Structures
Exercise 3
Let (G, *) be a group with neutral element e such that:
∀x ∈ G, x * x = e.
Show that * is commutative.
Exercise 4
Consider the groups (ℝ, +) and (ℝ*+, ⋅). We define the mapping:
f : ℝ → ℝ*+ defined by ∀x ∈ ℝ, f(x) = 4^x.
Show that f is a group isomorphism.
آخر تعديل: الجمعة، 5 سبتمبر 2025، 1:19 PM