For a permutation group G acting on set V, subset I of is said to be an intersecting if for every pair elements g,h∈I there exists v∈V such that g(v)=h(v). The intersection density ρ(G) transitive the maximum value quotient |I|/|Gv| where Gv stabilizer point and runs over all sets in G. If largest then have Erdős–Ko–Rado (EKR)-property, moreover, has strict-EKR-property size coset stabilizer. I...

The semi-direct product of arbitrary two monoids and a presentation for this product have received considerable attention, see for instance [12], [14] and [15]. In [15], Wang defined a trivialiser set of the Squier complex associated with this presentation. In this paper, as a main result, we discuss necessary and sufficient conditions for the standard presentation of the semi-direct product of...

Solution. The 11-Sylow subgroup is Z/11Z; the 5-Sylow subgroup is Z/5Z. By Sylow’s theorem, the 11-Sylow subgroup is normal. Hence, the group is a semi-direct product of its 5 and 11-Sylow subgroups. Since Aut(Z/11Z) = Z/10Z has a unique subgroup of order 5, there are up to isomorphism exactly two groups of order 55: the abelian group Z/55Z and the group with presentation ⟨x, y|x = y = 1, xyx−1...

The Frobenius group G belongs to an important class of groups that more than 100 years ago was defined by F. G. who proved is a semi-direct product normal subgroup K called kernel another non-trivial H the complement. In this case we show few classical finite can be