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Get Full Access to Contemporary Abstract Algebra - 8 Edition - Chapter 8 - Problem 1se
Get Full Access to Contemporary Abstract Algebra - 8 Edition - Chapter 8 - Problem 1se

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# A subgroup N of a group G is called a characteristic

ISBN: 9781133599708 52

## Solution for problem 1SE Chapter 8

Contemporary Abstract Algebra | 8th Edition

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Problem 1SE Problem 1SE

A subgroup N of a group G is called a characteristic subgroup if φ(N) 5 N for all automorphisms φ of G. (The term characteristic was first applied by G. Frobenius in 1895.) Prove that every subgroup of a cyclic group is characteristic.

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Chapter 1 – An Introduction to Biology  Discoveries affect every aspect of our lives including o Health and disease o Food o Relationships between humans and other organisms o Environment  Biology – science of life  Characteristics of living things o Cells  Complex, organized structure o Homeostasis  Maintain structure by regulation o Metabolism  All chemical reactions of cell o Response to environmental changes (stimuli) o Reproduction, growth, and development o Biological evolution  All life displays a common set of characteristics but there is diversity due to evolution  Evolution o Allows species to adapt to different environments  Di

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