For a finite noncyclic group G, let γ(G) be the smallest integer k such that G contains k proper subgroups H1,..., Hk with the property that every element of G is contained in Hig for some i∈{1,..., k} and g∈G. We prove that if G is a noncyclic permutation group of degree n, then γ(G)≤(n+2)/2. We then investigate the structure of the groups G with γ(G)=σ(G) (where σ(G) is the size of a minimal cover of G) and of those with γ(G)=2.
For a finite noncyclic group G, let gamma(G) be the smallest integer k such that G contains k proper subgroups H-1,..., H-k with the property that every element of G is contained in H-i(g) for some i is an element of {1, ..., k} and g is an element of G. We prove that if G is a noncyclic permutation group of degree n, then gamma(G) <= (n + 2)/2. We then investigate the structure of the groups G with gamma(G) = sigma(G) (where sigma(G) is the size of a minimal cover of G) and of those with gamma(G) = 2. (C) 2014 Elsevier Inc. All rights reserved.
Covers and normal covers of finite groups
GARONZI, MARTINO;
2015
Abstract
For a finite noncyclic group G, let gamma(G) be the smallest integer k such that G contains k proper subgroups H-1,..., H-k with the property that every element of G is contained in H-i(g) for some i is an element of {1, ..., k} and g is an element of G. We prove that if G is a noncyclic permutation group of degree n, then gamma(G) <= (n + 2)/2. We then investigate the structure of the groups G with gamma(G) = sigma(G) (where sigma(G) is the size of a minimal cover of G) and of those with gamma(G) = 2. (C) 2014 Elsevier Inc. All rights reserved.I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
