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The powers P n are normal subgroups of E(p), and the example groups are E(p,n) = E(p)/P n. E(p,n) has order p n+1 and nilpotency class n, so is a p-group of maximal class. When p = 2, E(2,n) is the dihedral group of order 2 n. When p is odd, both W(2) and E(p,p) are irregular groups of maximal class and order p p+1, but are not isomorphic.
A phosphoryl group is a trivalent >P(=O)− group, consisting of a phosphorus atom (symbol P) and an oxygen atom (symbol O), where the three free valencies are on the phosphorus atom. While commonly depicted as possessing a double bond (P=O) the bonding is in fact non-classical.
A classic example of an equivalence group is the vulva precursor cells (VPCs) of nematodes. In Caenorhabditis elegans self-fertilized eggs exit the body through the vulva. This organ develops from a subset of cell of an equivalence group consisting of six VPCs, P3.p-P8.p, which lie ventrally along the anterior-posterior axis. [5]
The P-type ATPases, also known as E 1-E 2 ATPases, are a large group of evolutionarily related ion and lipid pumps that are found in bacteria, archaea, and eukaryotes. [1] P-type ATPases are α-helical bundle primary transporters named based upon their ability to catalyze auto- (or self-) phosphorylation (hence P) of a key conserved aspartate residue within the pump and their energy source ...
This glossary of biology terms is a list of definitions of fundamental terms and concepts used in biology, the study of life and of living organisms.It is intended as introductory material for novices; for more specific and technical definitions from sub-disciplines and related fields, see Glossary of cell biology, Glossary of genetics, Glossary of evolutionary biology, Glossary of ecology ...
Another characterization is that a finite p-group in which there is a unique subgroup of order p is either cyclic or a 2-group isomorphic to generalized quaternion group. [13] In particular, for a finite field F with odd characteristic, the 2-Sylow subgroup of SL 2 ( F ) is non-abelian and has only one subgroup of order 2, so this 2-Sylow ...
A finite p-group G is said to be regular if any of the following equivalent (Hall 1959, Ch. 12.4), (Huppert 1967, Kap.III §10) conditions are satisfied: For every a, b in G, there is a c in the derived subgroup H ′ of the subgroup H of G generated by a and b, such that a p · b p = (ab) p · c p.
Isoclinism divides p-groups into families, and the smallest members of each family are called stem groups. A group is a stem group if and only if Z( G ) ≤ [ G , G ], that is, if and only if every element of the center of the group is contained in the derived subgroup (also called the commutator subgroup), Berkovich (2008 , p. 287).