Student Research Projects

Goursat's Other Theorem

$20.00 plus tax (Refund Policy)

Buy Article:

Abstract:

In an elementary undergraduate abstract algebra or group theory course, a student is introduced to a variety of methods for constructing and deconstructing groups. What seems to be missing from contemporary texts and syllabi is a theorem, first proved by Édouard Jean-Baptiste Goursat (1858-1936) in 1889, which completely describes the subgroups of a direct product and reveals beautiful connections among several elementary topics from group theory. We decompose the proof of Goursat's Theorem and its corollaries into a sequence of exercises which, when considered as a problem set for undergraduates, may be suitable for inclusion either in a mathematics capstone course, or even in the group theory section of a modern algebra final exam. On the other hand, the exercises may be strategically assigned to parallel the natural flow of the group theory presentation in abstract algebra so that by the end of the semester the theorem can be stated and proved without much difficulty.

Document Type: Research Article

DOI: http://dx.doi.org/10.4169/193113409X469569

Publication date: March 1, 2009

More about this publication?
Related content

Tools

Favourites

Share Content

Access Key

Free Content
Free content
New Content
New content
Open Access Content
Open access content
Subscribed Content
Subscribed content
Free Trial Content
Free trial content
Cookie Policy
X
Cookie Policy
ingentaconnect website makes use of cookies so as to keep track of data that you have filled in. I am Happy with this Find out more