0

# If d divides the order of a group does the group has a subgroup of order d?

Updated: 4/28/2022

Wiki User

16y ago

The general answer is no. Consider A4={(1),(12)(34),(13)(24),(14)(23),(123),(124),(132),(134),(142),(143),(234),(243)}. The subgroups of A4 are: A4, <(12)(34)>, <(13)(24)>, <(14)(23)>, <(123)>=<(132)>, <(124)>=<(142)>, <(134)>=<(143)>, <(234)>=<(243)>, {(1),(12)(34),(13)(24),(14)(23)}, {(1)}. The order of A4 is 12, the order of <(12)(34)>, <(13)(24)> and <(14)(23)> is 2, the order of <(123)>=<(132)>, <(124)>=<(142)>, <(134)>=<(143)> and <(234)>=<(243)> is 3, the order of {(1),(12)(34),(13)(24),(14)(23)} is 4, and the order of <(1)> is 1. Clearly there are no subgroups of order 6, but 6 definitely divides the order of A4. The statement is true for all finite abelian groups, and when d is a power of a prime (i.e., when d=pk for a prime p and a non-negative integer k).

Wiki User

16y ago

Earn +20 pts
Q: If d divides the order of a group does the group has a subgroup of order d?
Submit
Still have questions?
Related questions

### What group are Ukraine in in the Euro 2012?

They are in Group D with England, France and Sweden.They are in Group D with England, France and Sweden.They are in Group D with England, France and Sweden.They are in Group D with England, France and Sweden.They are in Group D with England, France and Sweden.They are in Group D with England, France and Sweden.They are in Group D with England, France and Sweden.They are in Group D with England, France and Sweden.They are in Group D with England, France and Sweden.They are in Group D with England, France and Sweden.They are in Group D with England, France and Sweden.

### What Vitamin D zones can the earths surface be separated into?

The earth's surface divides into four vitamin D zones with each repeating once. From highest to lowest point the order starts with High latitudes, Mid-latitudes, Subtropics, and Tropics then it

Cell Plate :D

### Which group are Germany in at the world cup?

Germany is in Group D. Group D: Germany, Australia, Serbia, Ghana

### In the World Cup 2010 which group is Germany in?

Germany is in Group D. Group D: Germany, Australia, Serbia, Ghana

### How the d-block group number relte to the number of outer s and d electrons?

The d-block group number corresponds to the number of outer d electrons in an element. For example, Group 4 elements in the d-block have 4 outer d electrons. The number of outer s electrons remains constant for d-block elements within a period.

### What are some seven letter words with 1st letter D and 3rd letter V and 5th letter D and 7th letter S?

According to SOWPODS (the combination of Scrabble dictionaries used around the world) there are 1 words with the pattern D-V-D-S. That is, seven letter words with 1st letter D and 3rd letter V and 5th letter D and 7th letter S. In alphabetical order, they are: divides

D

### What are some seven letter words with 1st letter D and 2nd letter I and 4th letter I and 5th letter D?

According to SOWPODS (the combination of Scrabble dictionaries used around the world) there are 3 words with the pattern DI-ID--. That is, seven letter words with 1st letter D and 2nd letter I and 4th letter I and 5th letter D. In alphabetical order, they are: divided divider divides

### What geographic landmark divides the two parts of Russia?

i have no freaking idea!! i want to know the same thing! D:

### What are some seven letter words with 1st letter D and 4th letter I and 5th letter D and 7th letter S?

According to SOWPODS (the combination of Scrabble dictionaries used around the world) there are 4 words with the pattern D--ID-S. That is, seven letter words with 1st letter D and 4th letter I and 5th letter D and 7th letter S. In alphabetical order, they are: decides derides divides dreidls

### What happens in a coup d?

An established organized group, most often military forcefully deposes the current leader in order to assume political leadership