1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Ulleksa [173]
3 years ago
13

Prove that an element has an order in an abelian group

Chemistry
1 answer:
Allushta [10]3 years ago
4 0

<span>2down votefavoriteI will quote a question from my textbook, to prevent misinterpretation:Let <span>GG</span> be a finite abelian group and let <span>mm</span> be the least common multiple of the orders of its elements. Prove that <span>GG</span> contains an element of order <span>mm</span>.I figured that, if <span><span>|G|=n</span><span>|G|=n</span></span>, then I should interpret the part with the least common multiple as <span><span>lcm(|<span>x1</span>|,…,|<span>xn</span>|)=m</span><span>lcm(|<span>x1</span>|,…,|<span>xn</span>|)=m</span></span>, where <span><span><span>xi</span>∈G</span><span><span>xi</span>∈G</span></span> for <span><span>0≤i≤n</span><span>0≤i≤n</span></span>, thus, for all such <span><span>xi</span><span>xi</span></span>, <span><span>∃<span>ai</span>∈N</span><span>∃<span>ai</span>∈N</span></span> such that <span><span>m=|<span>xi</span>|<span>ai</span></span><span>m=|<span>xi</span>|<span>ai</span></span></span>. I guess I should use the fact that <span><span>|<span>xi</span>|</span><span>|<span>xi</span>|</span></span> divides <span><span>|G|</span><span>|G|</span></span>, so <span><span>∃k∈N</span><span>∃k∈N</span></span> such that <span><span>|G|=k|<span>xi</span>|</span><span>|G|=k|<span>xi</span>|</span></span> for all <span><span><span>xi</span>∈G</span><span><span>xi</span>∈G</span></span>. I'm not really sure how to go from here, in particular how I should use the fact that <span>GG</span> is abelian.</span>
You might be interested in
Which of the following terms describes a piece of pure gold?
SCORPION-xisa [38]
Mixture would be the piece of pure gold. I don't know the explanation but the answer is mixture, I'm sure about that it is mixture, I read it somewhere.
4 0
3 years ago
Read 2 more answers
16) Which of the following elements is unique to nucleic acids when studying organic compounds?
FinnZ [79.3K]
The correct answer is: phosphorous
3 0
4 years ago
Read 2 more answers
I WILL GIVE BRAINLIEST ANSWER IN 5 MINS
snow_lady [41]

Physical Properties: Sodium bicarbonate is an odorless, white crystalline solid or fine powder. It has a slightly alkaline taste. Its density is 2.20 g mL-1 and it decomposes in temperatures above 50 ºC. The decomposition yields to sodium carbonate. It is highly soluble in water and poorly soluble in acetone and methanol. It is insoluble in ethanol.

Chemical Properties: Sodium bicarbonate is an amphoteric compounds, it means the compound has a character acids an basic at the same time.  It is highly soluble in water, resulting in a slighty alkaline solution.


i hope this part helps i will continue to research on Toothpaste's properties

6 0
3 years ago
Which description of salt is a physical property? (2 points)
jarptica [38.1K]

Product of mixing acids and bases describes salt is a physical property.

Product of mixing acids and bases

<u>Explanation:</u>

When an acid and a base are put together, they respond to kill the corrosive and base properties, creating a salt which portrays the physical property. The physical properties of table salt will be: Salt is a white cubic gem. At the point when the salt is unadulterated it clear.

It likewise shows up in white, dim or caramel shading relying on immaculateness. It is unscented yet has a solid salty taste. Fundamental salts contain the conjugate base of a feeble corrosive, so when they break down in the water, they respond with water to yield an answer with a pH more than 7.0.

8 0
3 years ago
A baby's crib would be about how long? 1 m 2 m 10 m 1 km
storchak [24]
-------2 meters-------
7 0
3 years ago
Read 2 more answers
Other questions:
  • Qué trabajo realiza una mujer si arrastra una caja y aplica una fuerza de 300 newtons, desplazándola a 2 metros?
    14·1 answer
  • Which ion has the largest radius?<br>1) Br-<br>2) Cl-<br>3) F-<br>4) I-​
    12·1 answer
  • Which reaction results in the greatest increase in entropy?
    15·2 answers
  • When the mass of the boron atom is calculated, the mass of the electrons is ignored. Why is the mass of the electrons ignored?
    11·2 answers
  • How many electrons are there in the only energy level of helium, a noble gas? * Two Three Six Eight​
    9·1 answer
  • For the net reaction: 2AB + 2C → A2 + 2BC, the following slow first steps have been proposed. AB → A + B 2C + AB → AC + BC 2AB →
    7·1 answer
  • You need to make an aqueous solution of 0.230 M aluminum nitrate for an experiment in a lab. Using a 250 ml volumetric flask how
    12·1 answer
  • At 0°c a bottle contains a 325 mL of water in its liquid state. What is the volume of the water after it freezes (at 0°C)?
    5·1 answer
  • Which of the following is a chemical change?
    6·1 answer
  • Help please please yes don’t scam
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!