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A group of order 189 is not simple

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#group-theory #sylow-theory #simple-groups
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Prove that there is no subgroup of index $6$ in a simple group of order $240$

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#abstract-algebra #simple-groups
598
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Discovery of the first Janko Group

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#abstract-algebra #group-theory #math-history #simple-groups
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Every finitely generated group has simple quotient

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#group-theory #simple-groups
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Center of Simple Abelian Group and Simple Nonabelian Group

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#abstract-algebra #group-theory #abelian-groups #simple-groups
204
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Finite groups with 15 or 16 conjugacy classes

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#group-theory #finite-groups #gap #simple-groups
549
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If $G$ is non-abelian and simple then $|G|$ divides $n_p!/2$

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#group-theory #sylow-theory #simple-groups
297
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Isomorphy of simple groups of order 360 : a proof with a presentation

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#reference-request #finite-groups #group-isomorphism #group-presentation #simple-groups
3.2k
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Any simple group of order $60$ is isomorphic to $A_5$

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#group-theory #reference-request #simple-groups
254
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Are all non-abelian groups not simple?

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#group-theory #abelian-groups #simple-groups
295
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Coprime action of simple groups

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#group-theory #finite-groups #online-resources #simple-groups
49
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Why do the integers modulo a composite positive number never form a simple group under addition?

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#group-theory #finite-groups #simple-groups
65
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Proving that in a finite abelian group, there exist a chain of subgroups so that the quotient is simple.

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#group-theory #abelian-groups #simple-groups
230
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Is non-abelian simple group complete?

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#group-theory #simple-groups #automorphism-group
151
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Conjugacy class with $1$ element in an Infinite Simple Group

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#abstract-algebra #group-theory #simple-groups #infinite-groups

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