# Tagged Questions

86 views

### If $G$ is a simple $f$ an homomorphism, and $A\lhd H$ is such that $[H:A]=2$, show $f(G) \subset A$

I'm stuck with the following problem. Can someone help me by providing a hint? Suppose $G$ is simple and let $f$ be an homomorphism between $G \to H$. If $\#G\ne2$, $A\lhd H$, and $[H:A]=2$. Then ...
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### hint with an exercise algebra

I'm stuck with the following I hope someone could help me. Let $N$ a normal subgroup of $G$. Show that if $[G:N]=4$, exists a normal subgroup $M$ of $G$ s.t. $[G:M]=2$. My idea: Since $G/N$ has ...
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69 views

### Suppose that the cyclic group $G$ acts on a set $S$

Suppose that the cyclic group $G$ acts on a set $S$ and $g_1$ and $g_2$ generate $G$. Show that $|$Fix $g_1|=|$Fix $g_2|$. We know that there is a function $\psi: G\times S\rightarrow S$ with the ...
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### What math will I need in order to learn Microsoft's UProve?

I'm studying Microsoft's UProve (independent studies at 35 years old) and forget most of the Math I learned in college. I intend to proceed and learn the contents of this chapter of this book but can ...
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### Factor groups and isomorphisms

I've somewhat recently been going back through one of my brother's old textbooks reviewing group theory. I'm up to a chapter called Factor-Group Computations and Simple Groups. The problems at the ...
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### Number of subgroups of prime order

I've been doing some exercises from my introductory algebra text and came across a problem which I reduced to proving that: The number of distinct subgroups of prime order $p$ of a finite group ...