This site is a member of a large collection of WebMathematica scripts written by the author. This web site demonstrates the subgroup of a cyclic group generated by a given single element.
To illustrate the structure of a cyclic group.
Target Student Population:
Abstract Algebra students.
Prerequisite Knowledge or Skills:
Knowledge of the definition of a cyclic group
Type of Material:
This site could be used for classroom demonstrations or student experimentation.
It requires a "Java-enabled" browser.
Evaluation and Observation
This applet is designed to show a user the algebraic structure of a finite cyclic group. The group itself is presented as a collection of dots on the circle. Pressing the ?Evaluate? button causes the applet to generate powers of an element with a preset step. Each step is shown as a chord connecting the dots on the circle. Choosing the ?Cosets? mode allows the user to see the cosets formation as well.
The Web page containing the applet could use an introduction section targeting potential students who plan to use the applet.
Potential Effectiveness as a Teaching Tool
This applet helps users understand the very basic algebraic structure of any finite cyclic group.
Instructors can use the applet as a part of in class demonstration of the definition and properties of a cyclic group, subgroup of a finite cyclic group, cosets formation, etc.
Because the user has the flexibility of choosing the order of the group and the step, it is easy to pick several examples with a prime or compound n.
The ?Animate? option is particularly helpful.
Ease of Use for Both Students and Faculty
The applet is extremely easy to use. It has only one button, two input lines, and three display options to choose. An average user should be able to begin using it immediately.