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Is there a way to describe all finite groups $G$ such that $\operatorname{Aut}(G) \cong S_3$?

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#group-theory #finite-groups #symmetric-groups #automorphism-group
149
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$SL(2,q)$ when $q$ is odd

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#abstract-algebra #finite-groups
966
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A finite group of even order, whose $2$-Sylow subgroups are cyclic, is not simple.

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#group-theory #finite-groups #cyclic-groups #sylow-theory #simple-groups
240
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Problem from Herstein's Topics in Algebra

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#abstract-algebra #group-theory #finite-groups
54
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What is the maximal $m$, such that $\mathbb{Z}_2^m \leq GL(n, 2)$?

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#abstract-algebra #group-theory #finite-groups #linear-groups
439
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Understanding Converse of Lagrange's theorem!

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#logic #finite-groups
2.6k
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Irreducible 2-Brauer characters of $S_5$

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#abstract-algebra #group-theory #finite-groups #representation-theory #characters
165
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Group of even order contains an element of order $2$ (Explanation)

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#abstract-algebra #group-theory #finite-groups
330
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Solvable, non-nilpotent group with nilpotent commutator subgroup

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#group-theory #finite-groups #solvable-groups #nilpotent-groups
1.6k
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How can I learn about the Monster group?

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#group-theory #soft-question #finite-groups
65
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How many elements of order $n$ does $\bigcup_n^\infty\{e^{\frac{2ik\pi}{n}}:0\leq k\leq n-1\}$ have?

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#group-theory #finite-groups
68
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How to represent the groups symbolically?

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#group-theory #finite-groups
53
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Does there exist a nearly immaculate group not of the form $C_{2^n}$?

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#abstract-algebra #group-theory #finite-groups #normal-subgroups
54
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About the set of periods of a group subset

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#group-theory #finite-groups #infinite-groups
680
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Why is 9 a generator of a group Z28?

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#finite-groups

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