Two non-isomorphic structures with the same number of elements

[white paper: pedagogical]

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For pedagogical purposes, we define a simple language to show that two different structures with the same number of elements in their universes are not isomorphic.

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

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 3, Article 234, 2021 [JE]

A simple group of order 168 is isomorphic to PGL(2,7)

[question]

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We present a sketch on a problem related to the isomorphism between the simple group of order 168 and the projective general linear group.

https://doi.org/10.31219/osf.io/ydex4

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 2, Article 114, 2020 [EK]

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

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

Mathematical tags of group theory

[microreview]

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I present a collection of mathematical results regarding group theory organized by tags.

https://doi.org/10.31219/osf.io/9xk68

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 2, Article 101, 2020 [DX]

Homomorphisms: a concise approach

[microreview]

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Some definitions and results of homomorphisms are presented within the fewest words and symbols as possible.

https://doi.org/10.31219/osf.io/7pgcs

Open Mathematics Collaboration

Op. J. Math. Phys.
Volume 2, Article 95, 2020 [DR]