Question

请翻译一道英文数学题并给出解答！！

(a) Draw a Cayley graph for the group G with generators a and b with
a^5 = b^4 = e and b^(-1)ab = a^2
(b) Show that the subgroup H generated by a and b^2 is isomorphic to the
dihedral group D5 of order 10.
(c) Find an element c in G of order 4 such that b and c generate G, and
draw the corresponding Cayley graph
A nonabelian group of order 20
这是前提条件

谢谢楼下的翻译，不过有点别扭，多少给我点启发

Answer 1

（一）画Cayley图，为G组与发电机A和B与
一^ 5 = B的^ 4 = E的和B ^ （ -1 ）抗体= ^ 2
（二）表明，该小组h所产生的A和B平方公尺，是同构的
二面体组的D5规程10 。
（三）找到一个元素C在克令4如B和C产生G和
制定相应的Cayley图