Find the subgroups of $Bbb{Z}_2 $ $×$ $Bbb{Z}_2$ $×$ $Bbb{Z}

Find the subgroups of $Bbb{Z}_2 $ $×$ $Bbb{Z}_2$ $×$ $Bbb{Z}_4$ [on hold]

How can I find all the subgroups of
$mathbb Z_2 times mathbb Z_2 times mathbb Z_4$ which are isomorphic to Klein-4 group? How can I approach to such a problem ?

Also how to find all proper subgroups of $mathbb Z_2 times mathbb Z_2 times mathbb Z_4$?

edited Dec 26 at 14:42

anomaly

17.3k42663

asked Dec 26 at 13:32

Henry

325

put on hold as off-topic by Shaun, anomaly, Saad, Dietrich Burde, drhab Dec 26 at 16:46

This question appears to be off-topic. The users who voted to close gave this specific reason:

"This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Shaun, anomaly, Saad, Dietrich Burde, drhab

If this question can be reworded to fit the rules in the help center, please edit the question.

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You'll find that simple "Here's the statement of my question, solve it for me" posts will be poorly received. What is better is for you to add context (with an edit): What you understand about the problem, what you've tried so far, etc.; something both to show you are part of the learning experience and to help us guide you to the appropriate help. You can consult this link for further guidance.
– Shaun
Dec 26 at 13:37

add a comment |

How can I find all the subgroups of
$mathbb Z_2 times mathbb Z_2 times mathbb Z_4$ which are isomorphic to Klein-4 group? How can I approach to such a problem ?

Also how to find all proper subgroups of $mathbb Z_2 times mathbb Z_2 times mathbb Z_4$?

edited Dec 26 at 14:42

anomaly

17.3k42663

asked Dec 26 at 13:32

Henry

325

put on hold as off-topic by Shaun, anomaly, Saad, Dietrich Burde, drhab Dec 26 at 16:46

This question appears to be off-topic. The users who voted to close gave this specific reason:

"This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Shaun, anomaly, Saad, Dietrich Burde, drhab

If this question can be reworded to fit the rules in the help center, please edit the question.

1

You'll find that simple "Here's the statement of my question, solve it for me" posts will be poorly received. What is better is for you to add context (with an edit): What you understand about the problem, what you've tried so far, etc.; something both to show you are part of the learning experience and to help us guide you to the appropriate help. You can consult this link for further guidance.
– Shaun
Dec 26 at 13:37

add a comment |

How can I find all the subgroups of
$mathbb Z_2 times mathbb Z_2 times mathbb Z_4$ which are isomorphic to Klein-4 group? How can I approach to such a problem ?

Also how to find all proper subgroups of $mathbb Z_2 times mathbb Z_2 times mathbb Z_4$?

edited Dec 26 at 14:42

anomaly

17.3k42663

asked Dec 26 at 13:32

Henry

325

How can I find all the subgroups of
$mathbb Z_2 times mathbb Z_2 times mathbb Z_4$ which are isomorphic to Klein-4 group? How can I approach to such a problem ?

Also how to find all proper subgroups of $mathbb Z_2 times mathbb Z_2 times mathbb Z_4$?

abstract-algebra group-theory group-isomorphism

edited Dec 26 at 14:42

anomaly

17.3k42663

asked Dec 26 at 13:32

Henry

325

edited Dec 26 at 14:42

anomaly

17.3k42663

asked Dec 26 at 13:32

Henry

325

edited Dec 26 at 14:42

anomaly

17.3k42663

edited Dec 26 at 14:42

anomaly

17.3k42663

edited Dec 26 at 14:42

anomaly

17.3k42663

asked Dec 26 at 13:32

Henry

325

asked Dec 26 at 13:32

Henry

325

asked Dec 26 at 13:32

Henry

325

put on hold as off-topic by Shaun, anomaly, Saad, Dietrich Burde, drhab Dec 26 at 16:46

This question appears to be off-topic. The users who voted to close gave this specific reason:

"This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Shaun, anomaly, Saad, Dietrich Burde, drhab

If this question can be reworded to fit the rules in the help center, please edit the question.

put on hold as off-topic by Shaun, anomaly, Saad, Dietrich Burde, drhab Dec 26 at 16:46

This question appears to be off-topic. The users who voted to close gave this specific reason:

"This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Shaun, anomaly, Saad, Dietrich Burde, drhab

If this question can be reworded to fit the rules in the help center, please edit the question.

1

You'll find that simple "Here's the statement of my question, solve it for me" posts will be poorly received. What is better is for you to add context (with an edit): What you understand about the problem, what you've tried so far, etc.; something both to show you are part of the learning experience and to help us guide you to the appropriate help. You can consult this link for further guidance.
– Shaun
Dec 26 at 13:37

add a comment |

1

You'll find that simple "Here's the statement of my question, solve it for me" posts will be poorly received. What is better is for you to add context (with an edit): What you understand about the problem, what you've tried so far, etc.; something both to show you are part of the learning experience and to help us guide you to the appropriate help. You can consult this link for further guidance.
– Shaun
Dec 26 at 13:37

You'll find that simple "Here's the statement of my question, solve it for me" posts will be poorly received. What is better is for you to add context (with an edit): What you understand about the problem, what you've tried so far, etc.; something both to show you are part of the learning experience and to help us guide you to the appropriate help. You can consult this link for further guidance.
– Shaun
Dec 26 at 13:37

add a comment |

1 Answer
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active

oldest

votes

Hint: The Klein 4 group consists of two (arbitrary) elements of order $2$, their sum, and the identity element.

answered Dec 26 at 13:35

Arthur

110k7105186

It's worth noting that their sum is also of order $2$.
– Shaun
Dec 26 at 15:32

add a comment |

1 Answer
1

active

oldest

votes

1 Answer
1

active

oldest

votes

Hint: The Klein 4 group consists of two (arbitrary) elements of order $2$, their sum, and the identity element.

answered Dec 26 at 13:35

Arthur

110k7105186

It's worth noting that their sum is also of order $2$.
– Shaun
Dec 26 at 15:32

add a comment |

Hint: The Klein 4 group consists of two (arbitrary) elements of order $2$, their sum, and the identity element.

answered Dec 26 at 13:35

Arthur

110k7105186

It's worth noting that their sum is also of order $2$.
– Shaun
Dec 26 at 15:32

add a comment |

Hint: The Klein 4 group consists of two (arbitrary) elements of order $2$, their sum, and the identity element.

answered Dec 26 at 13:35

Arthur

110k7105186

Hint: The Klein 4 group consists of two (arbitrary) elements of order $2$, their sum, and the identity element.

answered Dec 26 at 13:35

Arthur

110k7105186

answered Dec 26 at 13:35

Arthur

110k7105186

answered Dec 26 at 13:35

Arthur

110k7105186

answered Dec 26 at 13:35

Arthur

110k7105186

It's worth noting that their sum is also of order $2$.
– Shaun
Dec 26 at 15:32

add a comment |

It's worth noting that their sum is also of order $2$.
– Shaun
Dec 26 at 15:32

It's worth noting that their sum is also of order $2$.
– Shaun
Dec 26 at 15:32

add a comment |

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