Algebra

2012 Submissions

[3] viXra:2012.0189 [pdf] submitted on 2020-12-26 03:23:23

A Group of Order 1575 with a Normal Sylow 3-subgroup is Abelian

Authors: Henry Wong
Comments: 2 Pages.

In this paper we lay out the proof of this result in group theory using an old-fashioned approach.
Category: Algebra

[2] viXra:2012.0168 [pdf] replaced on 2020-12-25 08:42:01

The Elementary Proof of Fermat's Last Theorem (Complete)

Authors: Sattawat Suntisurat
Comments: 5 Pages.

Proof of Fermat's Last Theorem by using basic of algebra.
Category: Algebra

[1] viXra:2012.0056 [pdf] submitted on 2020-12-08 20:02:04

The 2N Conjecture on Spectrally Arbitrary Sign Patterns Is False

Authors: Yaroslav Shitov
Comments: 21 Pages.

A sign pattern is a matrix with entries in {+, −, 0}. An n × n sign pattern S is spectrally arbitrary if, for any monic polynomial f of degree n with real coefficients, one can replace the + and − signs in S with real numbers of the corresponding signs so that the resulting matrix has characteristic polynomial f. This paper refutes a long-standing conjecture with a construction of an n × n spectrally arbitrary sign pattern with less than 2n entries nonzero.
Category: Algebra