# Algebra

## 1903 Submissions

[3] **viXra:1903.0560 [pdf]**
*submitted on 2019-03-31 22:49:35*

### Direct Sum Decomposition of a Linear Vector Space

**Authors:** Anamitra Palit

**Comments:** 5 Pages.

The direct sum decomposition of a vector space has been explored to bring out a conflicting feature in the theory. We decompose a vector space using two subspaces. Keeping one subspace fixed we endeavor to replace the other by one which is not equal to the replaced subspace. Proceeding from such an effort we bring out the conflict. From certain considerations it is not possible to work out the replacement with an unequal subspace. From alternative considerations an unequal replacement is possible.

**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