Tata Institute of Fundamental Research
On the Group of Symmetries of the Rubik's Cube
Student Seminar
Speaker:
Nikhil S Mande
Organiser:
Rakesh Venkat
Date:
Friday, 14 Mar 2014, 14:30 to 16:00
Venue:
D-405 (D-Block Seminar Room)
(Scan to add to calendar)
Abstract:
Abstract: In this talk, we will prove that the group of symmetries of a standard (3x3x3) Rubik's cube is isomorphic to (\mathbb{Z}_37 \times \mathbb{Z}_2^{11}) \rtimes ((A_8 \times A_{12}) \rtimes Z_2). Due to limited time, some proofs may not be completely rigorous. We will also try to understand how the above structure suggests a natural commutator based approach to solving the Rubik's cube (and also how it generalizes to higher order cubes).
The talk will assume a very basic group theory background, namely knowledge of cyclic groups and direct products. We will define semidirect products and alternating groups through the course of the talk.
| Speaker: | Nikhil S Mande |
| Organiser: | Rakesh Venkat |
| Date: | Friday, 14 Mar 2014, 14:30 to 16:00 |
| Venue: | D-405 (D-Block Seminar Room) |
(Scan to add to calendar)
Abstract:
Abstract: In this talk, we will prove that the group of symmetries of a standard (3x3x3) Rubik's cube is isomorphic to (\mathbb{Z}_37 \times \mathbb{Z}_2^{11}) \rtimes ((A_8 \times A_{12}) \rtimes Z_2). Due to limited time, some proofs may not be completely rigorous. We will also try to understand how the above structure suggests a natural commutator based approach to solving the Rubik's cube (and also how it generalizes to higher order cubes).
The talk will assume a very basic group theory background, namely knowledge of cyclic groups and direct products. We will define semidirect products and alternating groups through the course of the talk.
The talk will assume a very basic group theory background, namely knowledge of cyclic groups and direct products. We will define semidirect products and alternating groups through the course of the talk.