A simple group of order 60 is isomorphic to a subgroup of S6

[microreview]

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We show that the permutation of six Sylow 5-subgroups by conjugation is a faithful action, so that G is isomorphic to a subgroup of S6.

https://doi.org/10.31219/osf.io/g43yj

Open Mathematics Collaboration

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Op. J. Math. Phys.
Volume 2, Article 113, 2020 [EJ]

3-cycle commutator

[microreview]

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We show within the maximum number of steps that if only one point is moved by two permutations, the commutator is a 3-cycle.

https://doi.org/10.31219/osf.io/kxnt8

Open Mathematics Collaboration

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Op. J. Math. Phys.
Volume 2, Article 106, 2020 [EC]

Cycle decomposition for the permutations of an infinite set

[original insight]

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We present two cycle decompositions for the permutations of an infinite set.

https://doi.org/10.31219/osf.io/u6zwt

Open Mathematics Collaboration

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Op. J. Math. Phys.
Volume 2, Article 92, 2020 [DO]