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Math417Midterm1_ReviewSheet

# Math417Midterm1_ReviewSheet - MATH 417 Midterm 1 Study...

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MATH 417 Midterm 1 Study Guide The main focus of the exam is on chapters 2, 3, and 4. Make sure you are familiar with the material in Chapter 0 but Chapter 0 was supposed to be a review of things you already knew so it will not be the main focus of the questions on the exam. Deﬁnitions you should know: Binary operation Group Abelian group Order of a group Order of an element Subgroup of a group Trivial subgroup Proper subgroup Cyclic subgroup Generator of a cyclic subgroup Center of a group Centralizer of an element of a group Theorems you should know the statements of and be able to use: Theorem 2.1(*) Theorem 2.2 (*) Theorem 2.3 (*) Theorem 3.1 One-Step Subgroup Test Theorem 3.2 Two-Step Subgroup Test Theorem 3.4 < a > Is a Subgroup (*) Theorem 3.5 Center is a Subgroup (*) Theorem 3.6 C ( a ) is a Subgroup (*) Theorem 4.1 (I presented this diﬀerently in lecture) Corollary 1 of 4.1 | a | =

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Math417Midterm1_ReviewSheet - MATH 417 Midterm 1 Study...

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