PlanetMath: subdirect product of groups

(more info)

Math for the people, by the people.

Main Menu

sections Encyclopædia
Papers
Books
Expositions

meta Requests (230)
Orphanage
Unclass'd
Unproven (519)
Corrections (16)
Classification

talkback Polls
Forums
Feedback
Bug Reports

downloads Snapshots
PM Book

information News
Docs
Wiki
ChangeLog
TODO List
Legalese
About

Entry average rating: No information on entry rating

subdirect product of groups

(Definition)

Let $(G_i)_{i\in I}$ be a family of groups. A subgroup of the direct product $\prod_{i\in I}G_i$ is said to be a subdirect product (or subcartesian product) of $(G_i)_{i\in I}$ if $\pi_i(H)=G_i$ for each $i\in I$ , where $\pi_i\colon\prod_{i\in I}G_i\to G_i$ is the -th projection map.

"subdirect product of groups" is owned by yark.

(view preamble)

See Also: residually $\mathfrak{X}$ , direct products of groups

Other names:

subdirect product, subcartesian product, subcartesian product of groups

Log in to rate this entry.
(view current ratings)

Cross-references: projection map, groups
There are 2 references to this entry.

This is version 4 of subdirect product of groups, born on 2004-12-13, modified 2006-09-16.
Object id is 6571, canonical name is SubdirectProductOfGroups.
Accessed 2429 times total.

Classification:

AMS MSC:

20E26 (Group theory and generalizations :: Structure and classification of infinite or finite groups :: Residual properties and generalizations)

Pending Errata and Addenda

None.

Discussion

forum policy

No messages.

Interact