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Can we find element of order $q^2-1$ in $\text{GL}_2(\mathbb{F}_q)$?

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#abstract-algebra #group-theory #finite-groups #finite-fields #general-linear-group
64
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how to show the orthogonal projection?

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#linear-algebra #functional-analysis #finite-groups
1.1k
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Show that a group of order $90$ is solvable

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#abstract-algebra #group-theory #finite-groups #sylow-theory
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Good introductory textbook for group theory

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#group-theory #reference-request #finite-groups
107
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Let $G$ be a finite abelian group with identity $e$. Prove that $\exists$ an element $x \in G$ such that ord y | ord x for all $y \in G$

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#abstract-algebra #group-theory #finite-groups
102
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Constructing minimal supplements with GAP

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#group-theory #finite-groups #gap #computer-algebra-systems
1.3k
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Is the regular representation just another way of saying the standard representation?

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#group-theory #finite-groups #representation-theory
486
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Find the number of $2$-Sylow subgroups in $GL_2(\mathbb F_5)$

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#abstract-algebra #group-theory #finite-groups #sylow-theory
1.2k
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Sylow Subgroups and Conjugation

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#abstract-algebra #group-theory #finite-groups #sylow-theory
111
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The order of elements in finite octonions

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#finite-groups #finite-fields #octonions
83
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Are given groups isomorphic

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#abstract-algebra #group-theory #finite-groups #symmetric-groups #group-isomorphism
136
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Subgroups needing more generators in number

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#abstract-algebra #group-theory #finite-groups
33
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Proving well-defineness of function which adds additional variable

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#group-theory #functions #finite-groups
60
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Possible orders of trace k elements in $SL_2(\mathbb F_q)$

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#finite-groups #finite-fields #gap
4.8k
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A group with 4 elements

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#abstract-algebra #group-theory #finite-groups

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