Covering the set of p-elements in finite groups by Sylow p-subgroups - ScienceDirect Skip to
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Let p be a prime and let G be a finite group which is generated by the set G p of its p-
elements. We show that if G is solvable and not a p-group, then the minimal number σ p (G) …

A cover of an associative (not necessarily commutative nor unital) ring R is a collection of
proper subrings of R whose set-theoretic union equals R. If such a cover exists, then the …

For a semigroup $ S $, the covering number of $ S $ with respect to semigroups, $\sigma_s
(S) $, is the minimum number of proper subsemigroups of $ S $ whose union is $ S $. This …

A cover of a unital, associative (not necessarily commutative) ring R is a collection of proper
subrings of R whose set-theoretic union equals R. If such a cover exists, then the covering …

Consider a nonsolvable finite group G, where R (G) represents the solvable radical of G. For
any element x in G, the solvabilizer of x in G, denoted by Sol_G (x), is defined as the set of all …

Sabatini (2024) defined a subgroup $ H $ of $ G $ to be an exponential subgroup if $ x^{| G:
H|}\in H $ for all $ x\in G $. Exponential subgroups are a generalization of normal (and …

A group partition is a group cover in which the components have trivial pairwise intersection.
Based on an idea of IM Isaacs in this paper we define the semi-partition of a group as a …

A cover of an associative (not necessarily commutative nor unital) ring R is a collection of
proper subrings of R whose set-theoretic union equals R. If such a cover exists, then the …

We will explore the nature of when certain finite groups have an equal covering, and when
finite groups do not. Not to be confused with the concept of a cover group, a covering of a …