Let G be a cyclic group generated by an element a.
a) Prove that if an = e for some n ∈ Z, then G is
finite.
b) Prove that if G is an infinite cyclic group then it contains
no nontrivial finite subgroups. (Hint: use part (a))
Given the set of vertices, determine whether the
quadrilateral is a rectangle, rhombus, or square:**Find the distance and slope or each line
segment.A (−2, 7), B (7,2), C (−2,−3), D (−11,2)This quadrilateral is a… A (Rhombus) B (Rectangle) C
(square)
Consider a rhombus that is not square (i.e., the four sides all have the same length, but the angles between sides is not 90°). Describe all the symmetries of the rhombus. Write down the Cayley table for the group of symmetries,
please prove this problem step by step. thanks
Prove that in every simple graph there is a path from every vertex
of odd degree to some other vertex of odd
degree.