# Algebra

## 1903 Submissions

[3] **viXra:1903.0560 [pdf]**
*replaced on 2019-06-24 21:35:25*

### Direct Sum Decomposition of a Linear Vector Space

**Authors:** Anamitra Palit

**Comments:** 6 Pages.

The direct sum decomposition of a vector space has been explored to bring out a conflicting feature in the theory. It has been proved that a subspace cannot have dimension less than a third of the dimension of the parent vector space.

**Category:** Algebra

[2] **viXra:1903.0367 [pdf]**
*submitted on 2019-03-21 04:32:57*

### The Klein Four-Group

**Authors:** Volker W. Thürey

**Comments:** 3 Pages.

We describe alternative ways to present the famous Klein four-group

**Category:** Algebra

[1] **viXra:1903.0099 [pdf]**
*submitted on 2019-03-05 06:31:22*

### Finite Faithful G-Sets Are Asymptotically Free

**Authors:** Pierre-Yves Gaillard

**Comments:** 3 Pages.

Let G be a finite nontrivial group, let X be a finite faithful G-set, let P^i(X) be the i-th power set of X, let n(i) be the number of points of P^i(X), let m(i) be the number of points of P^i(X) with non-trivial stabilizer, let k be the number of prime order subgroups of G, and set E(j):=2^j for any integer j. We prove that n(i)/m(i) is at least E(n(i-1)/4)/k for i>1.

**Category:** Algebra