Anti-CC-Groups and Anti-PC-Groups

Anti- CC-Groups and Anti-PC-Groups

A group G has Černikov classes of conjugate subgroups if the quotient group G/ coreG(NG(H)) is a Černikov group for each subgroup H of G. An anti-CC-group G is a group in which each nonfinitely generated subgroup K has the quotient group G/ coreG(NG(K)) which is a Černikov group. Analogously, a groupG has polycyclic-by-finite classes of conjugate subgroups if the quotient group G/coreG(NG(H)) i...

Automorphism Groups and Anti-pluricanonical Curves

We show the existence of an anti-pluricanonical curve on every smooth projective rational surface X which has an infinite group G of automorphisms of either null entropy or of type Z⋉Z, provided that the pair (X,G) is minimal. This was conjectured by Curtis T. McMullen (2005) and further traced back to Marat Gizatullin and Brian Harbourne (1987). We also prove (perhaps) the strongest form of th...

Groups and Ultra-groups

In this paper, in addition to some elementary facts about the ultra-groups, which their structure based on the properties of the transversal of a subgroup of a group, we focus on the relation between a group and an ultra-group. It is verified that every group is an ultra-group, but the converse is not true generally. We present the conditions under which, for every normal subultra-group of an u...

On Bipolar Anti Q- Fuzzy Groups

Anti-Homomorphism in Fuzzy Sub Groups