ﻻ يوجد ملخص باللغة العربية
Recent results of Qu and Tuarnauceanu describe explicitly the finite p-groups which are not elementary abelian and have the property that the number of their subgroups is maximal among p-groups of a given order. We complement these results from the bottom level up by determining completely the non-cyclic finite p-groups whose number of subgroups among p-groups of a given order is minimal.
Denote by $ u_p(G)$ the number of Sylow $p$-subgroups of $G$. It is not difficult to see that $ u_p(H)leq u_p(G)$ for $Hleq G$, however $ u_p(H)$ does not divide $ u_p(G)$ in general. In this paper we reduce the question whether $ u_p(H)$ divides $ u
In this paper, we show that all Coleman automorphisms of a finite group with self-central minimal non-trivial characteristic subgroup are inner; therefore the normalizer property holds for these groups. Using our methods we show that the holomorph an
We prove that a group homomorphism $varphicolon Lto G$ from a locally compact Hausdorff group $L$ into a discrete group $G$ either is continuous, or there exists a normal open subgroup $Nsubseteq L$ such that $varphi(N)$ is a torsion group provided t
Following Isaacs (see [Isa08, p. 94]), we call a normal subgroup N of a finite group G large, if $C_G(N) leq N$, so that N has bounded index in G. Our principal aim here is to establish some general results for systematically producing large subgroup
We define and study supercharacters of the classical finite unipotent groups of symplectic and orthogonal types (over any finite field of odd characteristic). We show how supercharacters for groups of those types can be obtained by restricting the su