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MATH 113 (12)

# Class Notes for MATH 113 at University of California - Berkeley

Introduction to Abstract Algebra

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##### 9-5 Lecture.docx

Def A binary algebraic structure is a set with a binary operation o...

Mathematics
MATH 113
Melnikov
##### 10-13 Lecture.docx

Fact Suppose A is an abelian group suppose B C are subgroups of A s...

Mathematics
MATH 113
Melnikov
##### 10-1 Lecture.docx

Def Direct Product of groups G GG is the set of ktuples g gggG unde...

Mathematics
MATH 113
Melnikov
##### 9-26 Lecture.docx

Even and odd permutationsObserveIf we have a cycle a aaa a a a a a ...

Mathematics
MATH 113
Melnikov
##### 9-3 Lecture.docx

Math 113More setsEmpty setwith a slash sometimes The unique set wit...

Mathematics
MATH 113
Melnikov
##### 9-8 Lecture.docx

GroupsCommutativeAee aa identityAaaaeNot using ae anymorejustaeA ne...

Mathematics
MATH 113
Melnikov
##### 9-15 Lecture.docx

Permutation GroupsLet x be a nonempty set Then S stands for the bin...

Mathematics
MATH 113
Melnikov
##### Week 3 Summary.docx

Finite Group Definition A group Gis finite if G is a finite set If ...

Mathematics
MATH 113
Melnikov
##### 10-6 Lecture.docx

Def Missed If K is a subgroup of G then G is normal if for all gG w...

Mathematics
MATH 113
Melnikov
##### 9-29 Lecture.docx

Recall the left coset is of gG is gHg h hH and H is a subgroup of G...

Mathematics
MATH 113
Melnikov
##### 9-10 Lecture.docx

Lemma For every x xex Proof Suppose z st xez Show xz XxexzEexzExzxz...

Mathematics
MATH 113
Melnikov
##### 9-12 Lecture.docx

Thm Every infinite cyclic group is isomorphic to Zand every finite ...

Mathematics
MATH 113
Melnikov
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