A note on groups with a large permodularly embedded subgroup

A SHORT NOTE ON ATOMS AND COATOMS IN SUBGROUP LATTICES OF GROUPS

In this paper we give an elementary argument about the atoms and coatoms of the latticeof all subgroups of a group. It is proved that an abelian group of finite exponent is strongly coatomic.

A note on quasi irresolute topological groups

In this study, we investigate the further properties of quasi irresolute topological groups defined in [20]. We show that if a group homomorphism f between quasi irresolute topological groups is irresolute at $e_G$, then $f$ is irresolute on $G$. Later we prove that in a semi-connected quasi irresolute topological group $(G,*,tau )$, if $V$ is any symmetric semi-open neighborhood of $e_G$, then...

Finite Groups With a Certain Number of Elements Pairwise Generating a Non-Nilpotent Subgroup

a short note on atoms and coatoms in subgroup lattices of groups

in this paper we give an elementary argument about the atoms and coatoms of the latticeof all subgroups of a group. it is proved that an abelian group of finite exponent is strongly coatomic.

A Note on Bilinear Groups of a Large Composite Order

We remark that the structure of bilinear groups of a large composite order (at least 1024 bits) could make group operation inefficient and lose the advantages of elliptic curve cryptography which gained mainly from smaller parameter size. As of 2013, the longest parameter recommended by NIST for elliptic curves has 571 bits. From the practical point of view, such an algebraic structure is unlik...