Mathematics Homework Solutions

Game Theory Problem dealing with personal choices

This is a problem dealing with game theory and personal choices

Cutting a Cake-Game Theory Problem dealing with personal choices

Problem dealing with cutting a cake and personal choices

Allocation between two persons of a list of items and their preference

This is an allocation of ten estates between two individuals

Statistics

"When the members of the Eye and I Photo Club discussed what type of film they had used during the past month, the following information was obtained; 77 used black and white film, 24 used only black and white, 65 used color, 18 used only color, 101 used black and white or color, 27 used infrared, 9 used all three types, and 8 d ...continues

Modern/Abstract Algebra Problem (Group Theory)

Show that the group generated by two elements where all the elements have order 3 is finite.

Modern/Abstract Algebra Problem (Group Theory)

What is the number of different conjugated classes of elements of order 2 in S_5.

Modern/Abstract Algebra Problem (Group Theory)

What are the normal subgroups in S_4.

Modern/Abstract Algebra Problem (Group Theory)

What are the normal subgroups in S_4. I would appreciate it if someone could also a thourough explanation of how they came up with the answer.

Central Extension Problem

Describe all nonisomorphic central extensions of Z_n by Z_2 x Z_2 meaning central group extensions of the following form 1 --> Z_n --> G --> Z_2 x Z_2 --> 1 Meaning, determine those nonisomorphic groups G that can be described by such an extension. Please also explain how you came up with the answer.

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