Tagged Questions

Use with the (group-theory) tag. A group is simple if it has no proper, non-trivial normal subgroups. Equivalently, its only homomorphic images are itself and the trivial group. The classification of finite simple groups is one of the great results of modern mathematics.

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mathieu group M23?

what is Mathieu group M23?is there an paper published about mathieu group M23?
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Maximal subgroups of almost simple groups with socle $PSL(2, q)$

Let $G$ be an almost simple group with socle $PSL(2,q)$ where $q=p^f>3$ is the $f$th power of some odd prime $p$, and $M$ a maximal subgroup of $G$. By http://arxiv.org/abs/math/0703685, except for ...
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Proper subgroup of simple groups

Not sure how to do this: Fix integer n>1. Prove there exist only finitely many simple groups containing proper subgroups of index smaller than or equal to n.
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Examples of profinite simple groups

The standard example of an infinite simple group is $A_\infty$, the direct limit of the alternating groups under the obvious injections. Are there also examples of infinite simple groups arising as ...
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Projective linear group - solvable

Let $q\geq 5$ and let PGL(2,q) be the projective general linear group. Question Do there exists a $q$ such that PGL(2,q) is solvable?
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Number of prime divisors of the order of $E_8(q)$.

I am trying to compute the number of prime divisors of the order of $E_8(q)$. I am interested in the general solution, but in particular, my problem calls for $q=p^{15}$ (for prime $p$) and \$q\equiv ...