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What is the relationship between solvable, nilpotent and transfer homomorphism?
I know some facts such as:
Nilpotent groups are solvable, $p$-groups are nilpotent, a finite group whose order is a product of distinct primes is solvable, and finite groups are nilpotent if and only ...
7
votes
1answer
145 views
An Intuitive Explanation of the Transfer Homomorphism
I just learned about the transfer homomorphism, and I am having trouble internalizing it. I am learning from 'A Course in the Theory of Groups', and I was hoping that perhaps someone had a more ...
6
votes
1answer
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What is the relationship between Mackey's theorem in character theory and Mackey's theorem in transfer theory?
Here are the statements of the two theorems. The first statement I took from a paper I have been reading, but I believe can also be found in Isaacs' Character Theory of Finite Groups as an exercise. ...
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Easy proof of trivial fusion implies normal p-complement
Theorem: Suppose G is a finite group with Sylow p-subgroup P. Then the following are equivalent:
The set K of elements of G of order relatively prime to p (the p′-elements) form a subgroup
If A and ...
6
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0answers
143 views
A problem in transfer theory
This is about problem 5B.1 page 157 in Isaacs' "Finite Group Theory" book. This chapter is definitely giving me trouble. The problem reads:
Let $G$ be a finite group, $P \in \operatorname{Syl}_p(G)$ ...
