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Let G be a finite group with more than one element. Show

Contemporary Abstract Algebra | 8th Edition | ISBN: 9781133599708 | Authors: Joseph Gallian ISBN: 9781133599708 52

Solution for problem 80E Chapter 3

Contemporary Abstract Algebra | 8th Edition

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Contemporary Abstract Algebra | 8th Edition | ISBN: 9781133599708 | Authors: Joseph Gallian

Contemporary Abstract Algebra | 8th Edition

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Problem 80E

Problem 80E

Let G be a finite group with more than one element. Show that G has an element of prime order.

Step-by-Step Solution:
Step 1 of 3

Chapter 49: Circulatory System COMPONENTS OF BLOOD  Blood­ aconnective tissue , composed of plasma o Functions: transportation, regulation, and protection  Blood is a fluid matrix o Plasma is 92% water o Contains:  Nutrients, wastes and hormones  Ions  Proteins  Formed elements o Formed elements of blood cells includered blood cells, white blood cells, and platelets  Red blood cells  Hemoglobin (binds and transports oxygen) found only in erythrocytes (red blood cells)vertebrates  Found in plasma of invertebrates  Leukocytes  Less than 1% of a blood cell  Granular and agranular  Platelets  Cell fragments that are pinched off larger cebone marrow  Part of thblood clotting system o Injury of a blood vessel cause the liver to release prothrombin, fibrinogen then converts to fibrin which aggregates and forms a clot  Formed elements come from stem cells o All elements are formed from thepluripotent cells o Hematopoiesis ­ production of blood cells in the bone marrow  Produces two types of stem cells  Lymphocytes from lymphoid stem cells  Myeloid ­ all other blood cells INVERTBRATE CIRCULATORY SYSTEM  Hydra and other cnidarians circulate water wigastrovascular cavity  Open and closed circulatory systems o Open­ open vessels, goes into the body cavity  Fluid that has no distinction between circulating fluid and extracellular fluid (hemolymph) o Closed­ blood doesn’t leave the blood vessels VERTEBRATE CIRCULATORY SYSTEMS  Fishes evolved a true chamber­pump heart o Two pumping chambers  First chamber consists of sinus, venosus, and atrium  Second chamber consists of ventricle, conus and arteriosus o Blood is pumped through the gills than to the rest of the body o Sinoatrial (SA) node ­ initiates the electrical impulse that produces a contraction in vertebrates  Acts aspacemaker for the heart  Double circulation is needed in amphibians o Pulmonary circulation ­ moves blood between heart and lungs o Systematic circulation ­ moves blood between the heart and the rest of the body  Amphibians and reptiles have modifications that keep the deoxygenated blood and oxygenated blood from mixing o Reptiles have a septum that subdivides the ventricle  Mammals, birds, and crocodilians have four­chambered hearts o Two atria and ventricles  Right atrireceives the deoxygenated blood from the body  Sends it to the right ventricle which pumps to the blood to the lungs  Left atrireceives the oxygenated blood from the lungs  Sends it to the left ventricle which pumps to the rest of the body o Two pairs of valves  Atrioventricular­ between the atria and the ventricles  Semilunar­ guard the exits from the ventricles to the arterial system THE FOUR­CHAMBERED HEART AND THE BLOOD VESSELS  Cardiac Cycle o Valves open and close as the heart restdiastole ) and contractssystole ) o Aorta ­ branches of systemic arteries that carry oxygen­rich blood from the left ventricle to the rest of the body  Arterial Blood Pressure o Sphygmomanometer ­ measures the blood pressure in the brachial artery found on the inside of the arm above the elbow o Systolic and Diastolic pressure  Systolic­ peak pressure when ventricles are contracting  Diastolic­ minimum pressure when the ventricles relax CHARACTERISTICS OF BLOOD VESSELS  Blood leaves through o Arteries toarterioles tocapillaries tovenules then to thveins  Arteries and veins are composed of four tissue layers o Endothelium, elastic fibers, smooth muscle, and connective tissue  Capillaries only have endothelium layer  Allows the exchange of gases and metabolites between the body and blood cells  Arteries and arterioles have evolved to withstand pressure o Smaller arteries and arterioles provide the greatest resistance to blood flow o Vasoconstriction ­ contraction of the smooth muscle layer; greatly increases resistance and decreases flow o Vasodilation ­ relaxation of the smooth muscle layer; decreases resistance but increases blood flow in organs o Vasoconstriction and vasodilation are important regulating body heat  Veins and Venules o Thinner layer of smooth muscles than arteries  Lymphatic System o The system consists of lymphatic capillaries, lymphatic vessels, lymph nodes, and lymphatic organs o Functions to carry away interstitial fluids that leave the cardiovascular system as well as the primary wall to the immune system o Lymph­ excess fluid in the tissues that drain in blind­ended lymph capillaries; also contain white blood cells  Progressively pass into larger lymphatic vessels o Lymph nodes contain germinal centers  Monitors lymphs and whatever should not be there  Site for lymphocyte activation REGULATION OF BLOOD FLOW AND BLOOD PRESSURE  Cardiac output o Volume of blood pumped by each ventricle per minute  Baroreceptor reflex o Keeps pressures in the brain constant o Detect any changes in the blood pressure  Blood volume is controlledfour hormones o Antidiuretic hormone ­ responds to the loss of fluid from the kidney o Aldosterone ­ has the kidney to absorb sodium and retain water in the blood o Atrial natriuretic hormone ­ secreted by the right atrium of the heart and causes sodium to be excreted to the urine (decreases blood pressure) o Nitric oxide ­ neurotransmitter, goes to the smooth muscle and dilute the blood vessels (decreases blood pressure)

Step 2 of 3

Chapter 3, Problem 80E is Solved
Step 3 of 3

Textbook: Contemporary Abstract Algebra
Edition: 8
Author: Joseph Gallian
ISBN: 9781133599708

The answer to “Let G be a finite group with more than one element. Show that G has an element of prime order.” is broken down into a number of easy to follow steps, and 20 words. This textbook survival guide was created for the textbook: Contemporary Abstract Algebra , edition: 8. This full solution covers the following key subjects: element, let, Group, Finite, order. This expansive textbook survival guide covers 34 chapters, and 2038 solutions. The full step-by-step solution to problem: 80E from chapter: 3 was answered by , our top Math solution expert on 07/25/17, 05:55AM. Contemporary Abstract Algebra was written by and is associated to the ISBN: 9781133599708. Since the solution to 80E from 3 chapter was answered, more than 260 students have viewed the full step-by-step answer.

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Let G be a finite group with more than one element. Show