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...

After WWII, ultra-nationalism, which was the leading ideology of wartime Japan, seemed to have lost its power to inspire the Japanese. In the 1960s, when the Japanese began to enjoy economic prosperity, Yukio Mishima, deploring that the Japanese were losing the traditional spirit and morality of the nation, was one of those citizens who felt a strong nostalgia for wartime Japan. In an attempt t...

In this contribution the discovery and properties of ultra-compact dwarf galaxies are presented, and their possible origin is discussed. This new type of galaxy resides in the cores of galaxy clusters. In the fundamental plane diagram of stellar systems, the luminosity and kinematical and structural properties of ultra-compact dwarfs locate them inbetween globular clusters and small compact ell...