math algebra (master )

Sep 14th, 2015
Anonymous
Category:
Engineering
Price: $35 USD

Question description

1) List all subgroups of S_3.

2) In S_5, how many elements x are there such that x^5=identity?

3) Let H be a subgroup of a group G. Find a bijection between the set of left cosets with respect to H and the set of right cosets with respect to H.

4) Let H be a subgroup of a group G.  If [G:H]=2, prove that H is a normal subgroup of G.

5) Let f be an homomorphism from the group of integers Z to itself. Show that f is completely determined by its action on 1: If f(1) = r, then f is multiplication by r; in other words, f(n) = rn for every integer n.

Tutor Answer

(Top Tutor) Ace_Tutor
School: Purdue University
PREMIUM TUTOR

Studypool has helped 1,244,100 students

Review from student
Anonymous
" Goes above and beyond expectations ! "
Ask your homework questions. Receive quality answers!

Type your question here (or upload an image)

1825 tutors are online

Brown University





1271 Tutors

California Institute of Technology




2131 Tutors

Carnegie Mellon University




982 Tutors

Columbia University





1256 Tutors

Dartmouth University





2113 Tutors

Emory University





2279 Tutors

Harvard University





599 Tutors

Massachusetts Institute of Technology



2319 Tutors

New York University





1645 Tutors

Notre Dam University





1911 Tutors

Oklahoma University





2122 Tutors

Pennsylvania State University





932 Tutors

Princeton University





1211 Tutors

Stanford University





983 Tutors

University of California





1282 Tutors

Oxford University





123 Tutors

Yale University





2325 Tutors