Locally finite groups with all subgroups either subnormal or nilpotent-by-Chernikov

Let G be a locally finite group satisfying the condition given in the title and suppose that G is not nilpotent-by-Chernikov. It is shown that G has a section S that is not nilpotent-by-Chernikov, where S is either a p-group or a semi-direct product of the additive group A of a locally finite field F by a subgroup K of the multiplicative group of F, where K acts by multiplication on A and generates F as a ring. Non-(nilpotent-by-Chernikov) extensions of this latter kind exist and are described in detail.

GROUPS THAT INVOLVE FINITELY MANY PRIMES AND HAVE ALL SUBGROUPS SUBNORMAL II

It is shown that if G is a hypercentral group with all subgroups subnormal, and if the torsion subgroup of G is a pi-group for some finite set pi of primes, then G is nilpotent. In the case where G is not hypercentral there is a section of G that is much like one of the well-known Heineken-Mohamed groups. It is also shown that if G is a residually nilpotent group with all subgroups subnormal whose torsion subgroup satisfies the above condition then G is nilpotent.

The Little Metropolis: Religion, Politics, & Spolia

There have been numerous councils throughout the Catholic Church?s history. From the First Council of Nicaea in 325 CE to Vatican II in 1962, only a few centuries have passed without any major church doctrinal change. Following hand in hand with changes in doctrine came the bifurcation of the Christian Church into the Roman CatholicChurch and the Orthodox Church. The first split came in 325 CE with Arianism. Arius of Alexandria and his followers did not agree with the Catholic Church?s viewpoint that the son, Jesus, should be on equal footing with the Father and the Holy Spirit. Constantine the Great brought the Arianism debate to the First Council of Nicaea,which declared Arianism a heretical religion. The following Catholic council?s decisions separated the two Churches even more, eventually creating the formal separation of the Church during the East-West Schism in the middle of the 11th century. Although the twoChurches constantly tried to unite, the Churches hit speed bumps along the way. Eventually, the 1274 Second Council of Lyons officially united the two Churches, even if only for an ephemeral time. At first glance, it might not seem that much resulted from the 1274 Second Council of Lyons. Almost immediately after the council?s ruling, the two Churches split again. Little is known as to why the 1274 Second Council of Lyons ultimately failed in its unification attempt. In this thesis, I will examine the churches of the Little Metropolis at Athens, Merbaka in the Argolid, and Agioi Theodoroi in Athens. In detailing the architectural features of these buildings, I will reconstruct the church building program in association with the 1274 Second Council of Lyons. I will also compare these churchesusing historical sources to keep the sociological, religious, political, and historical context accurate.