Visual Group Theory, Lecture 3.4: Direct products

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Visual Group Theory, Lecture 3.4: Direct products

There is a natural way to put a group structure on the Cartesian product of two groups. In this lecture, we introduce this concept algebraically, and show several different ways to visualize this, using tools such as Cayley diagrams and multiplication tables. We also look at subgroups and normal subgroups of direct products, and establish a few basic properties.

  1. Professor Macauley
  2. Mathematics
  3. Group theory
  4. Visual group theory
  5. Direct product
  6. Cayley diagram
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Комментарии
Автор

Are semidirect products covered in this series, if yes which lecture is it covered in?

arisioz
Автор

Are solutions to the home work or exercises in Nathan's book on VGT available anywhere?

dof
Автор

generators of exercise - a, b, c, ab, bc, ca, abc (these are cyclic) <b, c>, <a, b>, <a,c>,<c,ab>,<b,ac>,<a,bc>,<bc>,<bc,ac,ab> (non-cyclic) other two are identity and z2*z2*z2

smackronme
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The direct product of groups seems much akin to cartesian multiplication of graphs.

alanhere
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Are we sure there aren't 18 subgroups of Z2 * Z2 * Z2? Of course including the improper and trivial ones

davidefanchini
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16:40 Nooo! Don't burst my bubbles! T.T
BTW is the direct product commutative or not?

scitwi
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1, 1 example reminds me of emergent properties..

smackronme