I would like to know if every finite group is an extension of some group by another. Thanks
Is every finite group an extension?
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$\begingroup$
group-theory
finite-groups
group-extensions
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2Every group is an extension of itself by the trivial group. Or, do you mean something else? – 2012-06-08
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3Or of the trivial group by itself. =] – 2012-06-08
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5The group with one element is an extension of itself by itself, but that is not very interesting. A group with two elements is an extension of itself by a group of one element, but that is still not very interesting. To be an interesting extension, it must have a normal subgroup that has more than one element, but not all of the elements. The groups that are not interesting extensions are called simple groups. – 2012-06-08
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0@Jack: I think that would probably do for an answer (perhaps including an example of a simple group). – 2012-06-08