Abstract A generating set for a finite group G is minimal if no proper subset generates , and $m(G)$ denotes the maximal size of . We prove conjecture Lucchini, Moscatiello Spiga by showing that there exist $a,b> 0$ such any satisfies $m(G) \leqslant \cdot \delta (G)^b$ $\delta (G) = \sum _{p \text { prime}} m(G_p)$ where $G_p$ Sylow p -subgroup To do this, we first bound all almost simple g...

Abstract. Let L and M be two finite lattices. The ideal J(L,M) is a monomial ideal in a specific polynomial ring and whose minimal monomial generators correspond to lattice homomorphisms ϕ: L→M. This ideal is called the ideal of lattice homomorphism. In this paper, we study J(L,M) in the case that L is the product of two lattices L_1 and L_2 and M is the chain [2]. We first characterize the set...

Let G be a graph on n vertices and m edges. An edge is written xy (equivalently yx). A dominating set in G is a set of vertices D such that every vertex of G is either in D or is adjacent to some vertex of D. It is said to be minimal if it does not contain any other dominating set as a proper subset. For every vertex x let N [x] be {x} ∪ {y | xy ∈ E}, and for every S ⊆ V let N [S] := ⋃ x∈S N [x...