# Study Guides for All Professors

MIAMIOHMTH 421AllFall

## MTH 421 Study Guide - Final Guide: Integral Domain, Normal Subgroup, Commutative Ring

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Let x be a set & let f: x - x be a function. If f is injective, then x is surjective. If g has a subgroup of order 2 then g has an element of order 2.
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MIAMIOHMTH 421AllFall

## MTH 421 Study Guide - Final Guide: Conjugacy Class, Integral Domain, Normal Subgroup

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: g s(g/h) is the associated homomorphism, then describe the kernel of . principal ideal domain (pid) normal subgroup euclidean domain. (a b)= (a)^ (b)
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MIAMIOHMTH 421AllFall

## MTH 421 Study Guide - Midterm Guide: Equivalence Class, Abstract Algebra, Surjective Function

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Practice for exam - introduction to abstract algebra. The goal of this worksheet is to solidify concepts about sets, functions, equiva- lence relations
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MIAMIOHMTH 421AllFall

## MTH 421 Study Guide - Midterm Guide: Multiple Choice

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2n = n rotations including identity + n reflections n!/2: every group of order 5 is cyclic. 2n = n rotations including identity + n reflections n!/2: a
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MIAMIOHMTH 421AllFall

## MTH 421 Study Guide - Midterm Guide: Abelian Group, Multiple Choice, Positive Element

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Direct products cyclic: let ( g, *) be a group and a in g. the order of a is the least positive integer n such that a^n = e. Direct products nontrivial
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