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The pylorus is considered as having two parts, the pyloric antrum (opening to the body of the stomach) and the pyloric canal (opening to the duodenum). The pyloric canal ends as the pyloric orifice, which marks the junction between the stomach and the duodenum. The orifice is surrounded by a sphincter, a band of muscle, called the pyloric ...
Diagram showing parts of the stomach. The human stomach can be divided into four sections, beginning at the cardia followed by the fundus, the body and the pylorus. [8] [9] The gastric cardia is where the contents of the esophagus empty from the gastroesophageal sphincter into the cardiac orifice, the opening into the gastric cardia.
In mathematics, a Cayley graph, also known as a Cayley color graph, Cayley diagram, group diagram, or color group, [1] is a graph that encodes the abstract structure of a group. Its definition is suggested by Cayley's theorem (named after Arthur Cayley ), and uses a specified set of generators for the group.
Let T be a spanning tree for Y and define the fundamental group Γ to be the group generated by the vertex groups G x and elements y for each edge of Y with the following relations: y = y −1 if y is the edge y with the reverse orientation. y φ y,0 (x) y −1 = φ y,1 (x) for all x in G y. y = 1 if y is an edge in T. This definition is ...
Burnside's p a q b theorem states that if the order of a group is the product of one or two prime powers, then it is solvable, and so the group is not simple, or is of prime order and is cyclic. This rules out every group up to order 30 (= 2 · 3 · 5). If G is simple, and |G| = 30, then n 3 must divide 10 ( = 2 · 5), and n 3 must equal 1 (mod 3).
The zero group is a subgroup of every group, so for any abelian groups A and B, we have homomorphisms: and :. The pushout of these maps is the direct sum of A and B . Generalizing to the case where f and g are arbitrary homomorphisms from a common domain Z , one obtains for the pushout a quotient group of the direct sum; namely, we mod out by ...
These are also two resulting orders, the weak order and the Bruhat order, and corresponding Hasse diagrams. An important example is in the Coxeter groups. Further, some properties of this graph (the coarse geometry) are intrinsic, meaning independent of choice of generators.
V is the symmetry group of this cross: flipping it horizontally (a) or vertically (b) or both (ab) leaves it unchanged.A quarter-turn changes it. In two dimensions, the Klein four-group is the symmetry group of a rhombus and of rectangles that are not squares, the four elements being the identity, the vertical reflection, the horizontal reflection, and a 180° rotation.