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Group Theory : If in a finite group G an element a has exactly two conjugates, prove that G has a normal subgroup N ≠ e , G.

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If in a finite group G an element a has exactly two conjugates, prove that G has a normal subgroup N ≠ e , G

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Conjugates and permutation groups are investigated. The solution is detailed and well presented.

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Modern Algebra
Group Theory (CII)
Permutation Groups
Another Counting Principle

By:- Thokchom Sarojkumar Sinha

If in a finite group an element has exactly two conjugates, prove that has a normal ...

Solution provided by:
Thokchom Sarojkumar Sinha, MSc
Education
  • BSc, Manipur University
  • MSc, Kanpur University
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