People need to communicate each other in many emerging networks, i.e., in ad hoc networks. To ensure the security for group communication, group key management as a fundamental cryptographic primitive has been proposed. Although many proposals with regard to group key managemet have been introduced, they cannot be efficiently applied to realize secure subgroup and intergroup communications. In ...

let $r$ be an infinite ring. here we prove that if $0_r$ belongs to ${x_1x_2cdots x_n ;|; x_1,x_2,dots,x_nin x}$ for every infinite subset $x$ of $r$, then $r$ satisfies the polynomial identity $x^n=0$. also we prove that if $0_r$ belongs to ${x_1x_2cdots x_n-x_{n+1} ;|; x_1,x_2,dots,x_n,x_{n+1}in x}$ for every infinite subset $x$ of $r$, then $x^n=x$ for all $xin r$.

We study the distribution of the zeros near the central point for following families of primitive Dirichlet characters: (1) all primitive characters of conductor m, m a fixed prime; (2) all primitive characters of conductor m, m an odd square-free number with r factors (r fixed); (3) all primitive characters whose conductor is a square-free odd integer m ∈ [N, 2N ]. For these families the 1-lev...

A test element in a group G is an element g with the property that if f(g) = g for an endomorphism f of G to G then f must be an automorphism. A test element in a free group is called a test word. Nielsen gave the first example of a test word by showing that in the free group on x, y the commutator [x, y] satisfies this property. T. Turner recently characterized test words as those elements of ...

A substitution group G of degree n is said to be r-fold transitive if each of the n(n — 1) • • • (n—r + 1) permutations of its n letters taken r at a time is represented by at least one substitution of G. It is not sufficient to say that each of its possible sets of r letters is transformed into every one of these sets by the substitutions of G. For instance, in each of the semi-metacyclic grou...

Let F = 〈a, b〉 be a rank two free group. A word W (a, b) in F is primitive if it, along with another group element, generates the group. It is a palindrome (with respect to a and b) if it reads the same forwards and backwards. It is known that in a rank two free group any primitive element is conjugate either to a palindrome or to the product of two palindromes, but known iteration schemes for ...

Group signatures are a central cryptographic primitive that has received a considerable amount of attention from the cryptographic community. They allow members of a group to anonymously sign on behalf of the group. Membership is overseen by a designated group manager. There is also a tracing authority that can revoke anonymity by revealing the identity of the signer if and when needed, to enfo...

In our paper referred to above we claim to enumerate all …nite primitive linear groups of prime degree r over C with a nonabelian socle. However, the case where the socle is imprimitive was overlooked. In the present paper we deal with this case to complete the classi…cation. 2000 Mathematics Subject Classi…cation: 20H20 20C15 20C33 In the paper referred to above, we state a theorem (Theorem 1....