Let G be a finite group and H be a Hartley set of G. In this paper, we prove the existence and conjugacy of H -injectors of G and describe the characterization of injectors via radicals. As applications, some known results are directly followed. [ABSTRACT FROM AUTHOR]
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-1 α(x) ∈ G' for each x ∈ G. The set of all IA-automorphisms of G is denoted by (G). A group G is called semicomplete if and only if (G)=(G), where (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 pn (n ≤ 5), where p is an odd prime. This completes our work in 2011. [ABSTRACT FROM AUTHOR]
For a group G, by ...(G) we denote the number of conjugate classes of the non-cyclic subgroups of G. In this paper, the groups G with ...(G) = 3 are classified. [ABSTRACT FROM AUTHOR]
A k-nacci sequence in a finite group is a sequence of group elements x0,x1,...,xn,... for which, given an initial (seed) set x0,x1,...,xj-1, each element is defined by \[ x_{n}= \left\{\begin{array}{@{}l@{\quad}l@{}} x_{0}x_{1}\cdots x_{n-1}&\mbox{ for }j \le n 2. [ABSTRACT FROM AUTHOR]
The paper deals with the following problem: If a finite abelian 2-group is a direct product of its subsets of cardinality 4, does it follow that at least one of the factors is periodic? Two results are presented. In the first one, the structures of the group and the subsets are restricted but the size of the the group is not. In the second one, the group and the factors are general but the order of the group is 26. [ABSTRACT FROM AUTHOR]
Let p be a prime. The class of all p-soluble groups G such that every p-chief factor of G is cyclic and all p-chief factors of G are G-isomorphic is studied in this paper. Some results on T-, PT-, and PST-groups are also obtained. [ABSTRACT FROM AUTHOR]