Definitions : Groups , subgroups , cyclic groups , order of elements , normal subgroups, quotient groups , direct products of (sub)groups, isomorphisms, homomorphisms (groups, rings) , kernels, group actions, rings (all types), ideals (left, right, two-sided, prime, maximal )
Theorems : Lagrange's, Cayley's, 9.27, Isomorphism Theorems (1,2,3), Fundamental Theorem of Finite Abelian Groups, Cauchy's, Sylow's ( 1,2,3)
Final Exam shall include definitions, Theorems, Propositions, ... and problems from the following
Section 3.4 : 14 , 31,32, 33, 39, 40, 41,42, 45, 48, 49, 51, 53, 54
Section 4.4 :31, 32, 37, 38, 39
Section 5.3 : 2, 3, 7,13, 17, 23, 27, 29
Section 6.4 : 5, 6, 12, 15, 16, 19,
Section 9.3 : 2,7,8,15,16,26,27,28,34,35,36,41,45,47,48
Section 10.3: 4 (c,d) , 5, 10, 11,14(a)
Section 11.3 : 4,5,6,8,9,18,19
Section 12.3; 2, 3
Section 13.3; 1, 2, 3, 6, 7, 8
Section 14.4; 2
Section 15.3; 1, 3, 5, 6
Section 16.6: 1 (a,b,c,e) , 2, 3, 4
Theorems : Lagrange's, Cayley's, 9.27, Isomorphism Theorems (1,2,3), Fundamental Theorem of Finite Abelian Groups, Cauchy's, Sylow's ( 1,2,3)
Final Exam shall include definitions, Theorems, Propositions, ... and problems from the following
Section 3.4 : 14 , 31,32, 33, 39, 40, 41,42, 45, 48, 49, 51, 53, 54
Section 4.4 :31, 32, 37, 38, 39
Section 5.3 : 2, 3, 7,13, 17, 23, 27, 29
Section 6.4 : 5, 6, 12, 15, 16, 19,
Section 9.3 : 2,7,8,15,16,26,27,28,34,35,36,41,45,47,48
Section 10.3: 4 (c,d) , 5, 10, 11,14(a)
Section 11.3 : 4,5,6,8,9,18,19
Section 12.3; 2, 3
Section 13.3; 1, 2, 3, 6, 7, 8
Section 14.4; 2
Section 15.3; 1, 3, 5, 6
Section 16.6: 1 (a,b,c,e) , 2, 3, 4
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