An outpath of a vertex v in a digraph is a path starting at v such that vdominates the end vertex of the path only if the end vertex also dominates v. First we show thatletting D be a strongly connected semicomplete c...An outpath of a vertex v in a digraph is a path starting at v such that vdominates the end vertex of the path only if the end vertex also dominates v. First we show thatletting D be a strongly connected semicomplete c-partite digraph (c ≥ 3), and one of the partitesets of it consists of a single vertex, say v, then D has a c-pancyclic partial ordering from v,which generalizes a result about pancyclicity of multipartite tournaments obtained by Gutin in 1993.Then we prove that letting D be a strongly connected semicomplete c-partite digraph with c ≥ 3 andletting v be a vertex of D, then D has a (c - 1)-pan-outpath partly ordering from v. This resultimproves a theorem about outpaths in semicomplete multipartite digraphs obtained by Guo in 1999.展开更多
Let G be a group and G＇ be its commutator subgroup. An automorphism α of a group G is called an IA-automorphism if x^-1α（x） ∈G＇ for each x∈G. The set of all IA-automorphisms of G is denoted by IA（G）. A group...Let G be a group and G＇ be its commutator subgroup. An automorphism α of a group G is called an IA-automorphism if x^-1α（x） ∈G＇ for each x∈G. The set of all IA-automorphisms of G is denoted by IA（G）. A group G is called semicomplete if and only if IA（G） = Inn（G）, where Inn（G） is the inner automorphism group of G. In this paper we completely characterize semicomplete finite p-groups of class 2; we also classify all semicomplete finite p-groups of order p^n （n≤5）, where p is an odd prime. This completes our work in 2011.展开更多
文摘An outpath of a vertex v in a digraph is a path starting at v such that vdominates the end vertex of the path only if the end vertex also dominates v. First we show thatletting D be a strongly connected semicomplete c-partite digraph (c ≥ 3), and one of the partitesets of it consists of a single vertex, say v, then D has a c-pancyclic partial ordering from v,which generalizes a result about pancyclicity of multipartite tournaments obtained by Gutin in 1993.Then we prove that letting D be a strongly connected semicomplete c-partite digraph with c ≥ 3 andletting v be a vertex of D, then D has a (c - 1)-pan-outpath partly ordering from v. This resultimproves a theorem about outpaths in semicomplete multipartite digraphs obtained by Guo in 1999.
文摘Let G be a group and G＇ be its commutator subgroup. An automorphism α of a group G is called an IA-automorphism if x^-1α（x） ∈G＇ for each x∈G. The set of all IA-automorphisms of G is denoted by IA（G）. A group G is called semicomplete if and only if IA（G） = Inn（G）, where Inn（G） is the inner automorphism group of G. In this paper we completely characterize semicomplete finite p-groups of class 2; we also classify all semicomplete finite p-groups of order p^n （n≤5）, where p is an odd prime. This completes our work in 2011.
