A new proof of Rédei’s theorem

Abstract

If a finite abelian group is expressed as the product of subsets each of which has a prime number of elements and contains the identity element, then at least one of the factors is a subgroup. This theorem was proved by L. Redei in 1965. In this paper we will give a shorter proof.

Simulated factorizations II

“…We first observe that certain key results of R6dei [6] We now generalize to multiple factorizations using multisets a result first stated by R6dei [5] but whose first complete proof was given by Wittmann [7]. We refer also to Corrfidi and Szab6 [2]. …”

Factoring Elementary p-Groups for p ≤ 7

“…By Lemma 5 of [2], in the factorization the factor For p = 7 the graph Γ has 7 3 = 343 nodes. The inspection gave 140 cliques of size 7 2 = 49.…”

Factorization Results with Combinatorial Proofs

“…As a consequence, U i 6 D V i . By Lemma 5 of [1], in the factorization (1) the factor A 1 can be replaced by U 1 , V 1 to get the factorizations…”

“…By Lemma 5 of [1], in the factorization (1) the factor A 1 can be replaced by U 1 to get the factorization G D U 1 A 2 A n . In this factorization the factor A 2 can be replaced by U 2 to get the factorization G D U 1 U 2 A 3 A n .…”