background: gap junctions (gjs) provide direct intercellular communications that are formed by hexameric protein subunits, called connexin (cx). the role of cxs in epileptogenesis has not received sufficient attention. hippocampus with critical function in epileptogenesis has a wide network of gjs. we examined the protein expression levels of hippocampal cx36 (the prominent cx present between g...

Geometric methods proposed by Stallings [46] for treating finitely generated subgroups of free groups were successfully used to solve a wide collection of decision problems for free groups and their subgroups [3, 19, 29, 30, 36, 41, 49]. In the present paper we employ the generalized Stallings’ methods, developed by the author in [32], to solve various algorithmic problems concerning finitely g...

A subgroup H of a group G is contranormal if HG=G. In finite groups, there are no proper subgroups, then the nilpotent but this not true in infinite groups as well-known Heineken–Mohamed show. We call such without subgroups “contranormal-free.” article, we prove various results concerning contranormal-free proving, for example that locally generalized radical which have section rank hypercentral.

Let Φ̃ be a root system of type F4, and let G be a group generated by non-trivial subgroups Ar, r ∈ Φ̃, satisfying some generalized Steinberg relations, which are also satisfied by root subgroups corresponding to a Moufang octagon. These relations can be considered as a generalization of the element-wise commutator relations in Chevalley groups. The Steinberg presentation specifies the groups sat...