Article
Licensed
Unlicensed
Requires Authentication
On finite groups close to completely factorisable groups
-
V. A. Vedernikov
Published/Copyright:
June 28, 2007
A subgroup H of a group G is called complemented in G if a subgroup K exists in G such that G = HK and H ∩ K = 1. A group is called completely factorisable if each subgroup of the group is complemented.
Let D(G) be the subgroup of a group G generated by all subgroups of G which have no complements in G, Z(G) be the centre of the group G, and Φ(G) be the Frattini subgroup of the group G. If all subgroups of G are complemented in G, then we set D(G) = 1. Each cyclic subgroup of the Frattini subgroup Φ(G) of the group G has no complement in G, therefore Φ(G) ⊆ D(G).
In the paper, we obtain a complete description of the structure of a finite group G such that D(G) ⊆ Z(G)Φ(G).
Published Online: 2007-06-28
Published in Print: 2007-07-20
Copyright 2007, Walter de Gruyter
You are currently not able to access this content.
You are currently not able to access this content.
Articles in the same Issue
- The compound Poisson distribution of the number of matches of values of a discrete function of s-tuples in segments of a sequence of random variables
- On stability of an efficient solution of a vector Boolean problem of maximisation of absolute values of linear functions
- Optimal logarithmic functions for lifting of a solution of an exponential congruence
- On the number of independent sets in graphs with fixed independence number
- Homomorphisms and endomorphisms of linear and alinear quasigroups
- On finite groups close to completely factorisable groups
- Non-asymptotic bounds for probabilities of the rank of a random matrix over a finite field
- On representation of k-valued logic functions by a sum of products of subfunctions
- A lower bound for the 4-satisfiability threshold
- A Markov chain of order s with r partial connections and statistical inference on its parameters
Articles in the same Issue
- The compound Poisson distribution of the number of matches of values of a discrete function of s-tuples in segments of a sequence of random variables
- On stability of an efficient solution of a vector Boolean problem of maximisation of absolute values of linear functions
- Optimal logarithmic functions for lifting of a solution of an exponential congruence
- On the number of independent sets in graphs with fixed independence number
- Homomorphisms and endomorphisms of linear and alinear quasigroups
- On finite groups close to completely factorisable groups
- Non-asymptotic bounds for probabilities of the rank of a random matrix over a finite field
- On representation of k-valued logic functions by a sum of products of subfunctions
- A lower bound for the 4-satisfiability threshold
- A Markov chain of order s with r partial connections and statistical inference on its parameters
