(a)
Whether the set
(b)
Whether the set
(c)
Whether the set
(d)
Whether the set
(e)
Whether the set
(f)
Whether the set
(g)
Whether the set
(h)
Whether the set
Want to see the full answer?
Check out a sample textbook solutionChapter 3 Solutions
Elements Of Modern Algebra
- In Exercises 15 and 16, the given table defines an operation of multiplication on the set S={ e,a,b,c }. In each case, find a condition in Definition 3.1 that fails to hold, and thereby show that S is not a group. See Figure 3.7 e a b c e e a b c a e a b c b e a b c c e a b carrow_forwardIn Exercises and, the given table defines an operation of multiplication on the set. In each case, find a condition in Definition that fails to hold, and thereby show that is not a group. 15. See Figure.arrow_forwardDecide whether each of the following sets is a subgroup of G={ 1,1,i,i } under multiplication. If a set is not a subgroup, give a reason why is not. a. { 1,1 } b. { 1,i } c. { i,i } d. { 1,i }arrow_forward
- What relationship subset, intersect, disjoint, or equivalent can be used to characterize the two shown in the Venn Diagram?arrow_forward42. For an arbitrary set , the power set was defined in Section by , and addition in was defined by Prove that is a group with respect to this operation of addition. If has distinct elements, state the order of .arrow_forwardFind the order of each of the following elements in the multiplicative group of units . for for for forarrow_forward
- Find subgroups H and K of the group S(A) in example 3 of section 3.1 such that HK is not a subgroup of S(A). From Example 3 of section 3.1: A=1,2,3 and S(A) is a set of all permutations defined on A.arrow_forwardIn Exercises and , part of the multiplication table for the group is given. In each case, complete the table. 13. See Figure . Figurearrow_forwardLet H and K be subgroups of a group G and K a subgroup of H. If the order of G is 24 and the order of K is 3, what are all the possible orders of H?arrow_forward
- In Exercises 13 and 14, part of the multiplication table for the group G={ a,b,c,d } is given. In each case, complete the table. See Figure 3.10. abcdabacad Figure 3.10arrow_forwardIf H and K are subgroups of G, H|= 16 and IKl=28 then a possible value of |HNK| is * 8. O 16 O 4arrow_forwardQ1. Examine whether or not the following listed subsets form a subgroup. (write all details) 1. H, = {e, (1432), (1234), (13) • (24)}, 2. H2 = {0,4,8,12,16,20,24,28,32}, 3. H3 = {r, r3, l4,l3), from the group (P,). from the group (Z36, +36) from the group of symmetric (S3,0) %3D 4. H4 = { ),a, b,c € R, a + 0 # c (lower bound)} from the group of non-singular matrices (M2x2 (R) X). 5. Hg = {x € G: x? = x}, from the abelian group (G,+). %3Darrow_forward
- Elements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning