There exist finite groups that are semidirect products of cyclic groups and are not determined by their endomorphism semigroups in the class of all groups [10].

On the definability of a semidirect product of cyclic groups by its endomorphism semigroup.

k] - the cyclic group of order k) are determined by their endomorphism semigroups in the class of all groups.

Semidirect products of generalized quaternion groups by a cyclic group.

Among the topics are greatest common divisors, integer multiples and exponents, quotients of polynomial rings, divisibility and factorization in integral domains, subgroups of

cyclic groups, cosets and Lagrange's theorem, the fundamental theorem of finite abelian groups, and check digits.

Popular choices for the group G in discrete logarithm cryptography are the cyclic groups [[].

Let G be a finite cyclic group, and [theta] [member of] G be a generator of G.

Let G = ([theta]) be a cyclic group of order n, and let a and b be elements of G.

The discrete logarithm problem (DPL) in a finite cyclic group G, with a generator [theta] and an element g, is to find the integer a; 0 [less than or equal to] a [less than or equal to] [absolute value of G]-1, such that g = [[theta].

Polyrotaxanes are polymers with

cyclic groups threaded onto a polymer chain.

They focus mainly on

cyclic groups, even though some of the results become trivial.

Mathematicians and scientists discuss such matters as rigid abelian groups and the probabilistic method, looking for indecomposable right bounded complexes, kernel modules of cotorsion pairs, upper cardinal bounds for absolute structures, subgroups of totally projective primary abelian groups and direct sums of

cyclic groups, generic endomorphisms of homogeneous structures, special pairs and automorphisms of centerless groups, and some results on the algebraic entropy.