Test 1
Definition of groups, subgroups, cyclic groups, order of an element, order of a group
Propositions, Theorem: 3.17, 3.18, 3.19, 3.20, 3.21, 3.22, 3.23. 3.30, 3.31
Propositions, Theorem: 4.9, 4.10, 4.11, 4.12, 4.13,
Section 3.4, 7, 8, 9, 10,13 14, 15, 25, 27, 31, 32, 33, 39, 41, 42, 48, 49, 51, 53
Section 4.4, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 23, 27, 28,
Test 2
Proposition 5.8., Theorem 5.9. , Proposition 5.12. , Theorem 5.23
Section 5.3
2, 3, 8,10,13,14,25,26(b,c)
Lemma 6.3, Theorem 6.4, Theorem 6.8, Proposition 6.9, Theorem 6.10, Corollary 6.11, Corollary 6.12, Corollary 6.13, Theorem 6.16
Section 6.4
2,5,6,9,10,11,12,13,15,16,17,18,19
Theorem 9.6, Theorem 9.7 , Theorem 9.8 , Theorem 9.12, Proposition 9.13, Theorem 9.17, Theorem 9.21, Definition of internal direct product , Theorem 9.27
Section 9.3
1,2,3,4,5,6,8,9,12,14,16,17,18,22,23,24,25,36,37,38,39,41,42,43,46,52
Test 3 shall include definitions, Theorems, Propositions, ... and problems from the following
Chapter 10.
Normal subgroups, quotient group,
Theorem 10.3, Theorem 10.4, Theorem 10.11,
Section 10.3 : 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14
Chapter 11.
Group homomorphisms,
Proposition 11.4, Theorem 11.5, Theorem 11.10, Theorem 11.12, Theorem 11.13, Theorem 11.14
Section 11.3 : 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,13, 18
Chapter 13.
(Sub)normal series , isomorphic series, composition series, principal series, solvable groups
Theorem 13.4, Theorem 13.18
Section 13.3 : 2, 3, 4, 8
Final Exam shall include definitions, Theorems, Propositions, ... and problems from the following
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)
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 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
Definition of groups, subgroups, cyclic groups, order of an element, order of a group
Propositions, Theorem: 3.17, 3.18, 3.19, 3.20, 3.21, 3.22, 3.23. 3.30, 3.31
Propositions, Theorem: 4.9, 4.10, 4.11, 4.12, 4.13,
Section 3.4, 7, 8, 9, 10,13 14, 15, 25, 27, 31, 32, 33, 39, 41, 42, 48, 49, 51, 53
Section 4.4, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14, 23, 27, 28,
Test 2
Proposition 5.8., Theorem 5.9. , Proposition 5.12. , Theorem 5.23
Section 5.3
2, 3, 8,10,13,14,25,26(b,c)
Lemma 6.3, Theorem 6.4, Theorem 6.8, Proposition 6.9, Theorem 6.10, Corollary 6.11, Corollary 6.12, Corollary 6.13, Theorem 6.16
Section 6.4
2,5,6,9,10,11,12,13,15,16,17,18,19
Theorem 9.6, Theorem 9.7 , Theorem 9.8 , Theorem 9.12, Proposition 9.13, Theorem 9.17, Theorem 9.21, Definition of internal direct product , Theorem 9.27
Section 9.3
1,2,3,4,5,6,8,9,12,14,16,17,18,22,23,24,25,36,37,38,39,41,42,43,46,52
Test 3 shall include definitions, Theorems, Propositions, ... and problems from the following
Chapter 10.
Normal subgroups, quotient group,
Theorem 10.3, Theorem 10.4, Theorem 10.11,
Section 10.3 : 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 14
Chapter 11.
Group homomorphisms,
Proposition 11.4, Theorem 11.5, Theorem 11.10, Theorem 11.12, Theorem 11.13, Theorem 11.14
Section 11.3 : 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,13, 18
Chapter 13.
(Sub)normal series , isomorphic series, composition series, principal series, solvable groups
Theorem 13.4, Theorem 13.18
Section 13.3 : 2, 3, 4, 8
Final Exam shall include definitions, Theorems, Propositions, ... and problems from the following
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)
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 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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