[knowledge base]
CAYLEY’s THEOREM, the SYMMETRIC GROUP THEOREM, and their underlying definitions are presented in this white paper (knowledge base = http://omkb.org).
https://doi.org/10.31219/osf.io/63pmy
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 3, Article 223, 2021 [IT]
[pedagogical]
We translate the proof of the theorem stated in the title, accomplished by Prover9, into a human readable form.
https://doi.org/10.31219/osf.io/wsbne
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 3, Article 222, 2021 [IS]
[knowledge base]
CYCLIC GROUP and its underlying definitions are presented in this white paper (knowledge base).
https://doi.org/10.31219/osf.io/nvkab
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 3, Article 215, 2021 [IL]
[microreview]
We prove that a subgroup has the same number of left and right cosets.
https://doi.org/10.31219/osf.io/t4snh
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 2, Article 137, 2020 [FH]
[microreview]
We prove the proposition addressed in the title of this paper.
https://doi.org/10.31219/osf.io/34vbp
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 2, Article 117, 2020 [EN]
[question]
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]
[microreview]
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]
[microreview]
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
Op. J. Math. Phys.
Volume 2, Article 106, 2020 [EC]
[microreview]
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]
[microreview]
Some definitions and results for counting with groups are presented within the fewest words and symbols as possible.
https://doi.org/10.31219/osf.io/9hdwj
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 2, Article 100, 2020 [DW]
[microreview]
The purpose of this paper is organizational for it presents a list of notations and mathematical definitions used in some results of abstract algebra.
https://doi.org/10.31219/osf.io/u8yx2
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 2, Article 98, 2020 [DU]
[microreview]
Some definitions and results of group actions are presented within the fewest words and symbols as possible.
https://doi.org/10.31219/osf.io/9dt34
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 2, Article 97, 2020 [DT]
[microreview]
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]
[microreview]
Some definitions and results of subgroups are presented within the fewest words and symbols as possible.
https://doi.org/10.31219/osf.io/wcaez
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 2, Article 94, 2020 [DQ]
[microreview]
Some definitions and results of groups are presented within the fewest words and symbols as possible.
https://doi.org/10.31219/osf.io/bfyhm
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 2, Article 93, 2020 [DP]
[original insight]
We present two cycle decompositions for the permutations of an infinite set.
https://doi.org/10.31219/osf.io/u6zwt
Open Mathematics Collaboration
Op. J. Math. Phys.
Volume 2, Article 92, 2020 [DO]
Open Journal of Mathematics and Physics 