Let G be a group with identity e and let Prove that the setcalled the centralizer of a in G, is a subgroup of G.

Week1BIOB170Notes ClassifyingLifeandPhylogenetic Kingdoms • Plants • Animals • In1960sPlantae,Fungi,Animalia,Protista,Monera Domains • Moreinclusivethankingdoms • Bacteria-Monera • Archaea-Monera • Eukarya-Protista,Plantae,FungiandAnimalia o Allhaveacommonancestor o Archaeaandeukaryaaremorecloselyrelated HierarchicalClassifications 1. Kingdom 2. Phylum 3. Class 4. Order 5. Family 6. Genus 7. SpecificEpithet Phylogenetics • Studyofevolutionaryrelationships • Showssupergroups • Branchpoint-wheretwonewspeciesareformed • Ancestralgroup-theancestoroftwonewspecies • Monophyletic-