Answer to Question #87220 in Abstract Algebra for arjun singh

Question

a)Let S be a set with n elements, n >= 3 . Let B be the set of bijective mappings of S
onto itself.
i) Check whether (B, o) is a group or not.
ii) Give the cardinality of the set B .
iii) Is o commutative? Give reasons for your answer.
b) Check whether or not H = {x∈R*|x =1 or x∉Q } is a subgroup of ( R*,.) . Also
check whether K = {x∈R*|x>=1} is a subgroup of R* or not.
c) Let U(n) ={x∈N|1<+x<n,(x,n)=1}. Show that U(n) is a group w.r.t.
multiplication modulo n . Also show that U(14) is cyclic and U(20) is not
cyclic.
d) Obtain the centre of Q_8 and two distinct right cosets of Z(Q_8 ) in Q_8.

Answer 1

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