GroupDirectProduct

A name from the enumeratio catalogue with no kernel of its own yet; this page carries its crosswalk only.

Mapped through to oscar for the oracle; not yet written up here.

GroupDirectProduct(...)Mapped through to oscar for the oracle; not yet written up here.

Typed signatures

Type	Package	Applies
(expression<CyclicGroup> | expression<DihedralGroup> | expression<GroupDirectProduct>, expression<CyclicGroup> | expression<DihedralGroup> | expression<GroupDirectProduct>) -> expression<GroupDirectProduct>	groupalgebra	always

Domain: Oracle

Examples

Basic #

$2 \cdot 6 = 12$

live ↗

In$\mathrm{GroupOrder}(\mathrm{GroupDirectProduct}(\mathrm{CyclicGroup}(2), \mathrm{DihedralGroup}(3)))$Out$12$

live ↗

In$\mathrm{GroupIsAbelian}(\mathrm{GroupDirectProduct}(\mathrm{CyclicGroup}(2), \mathrm{CyclicGroup}(3)))$Out$\mathrm{True}$

About

Examples	2
Checked against	Wolfram Language 2 agreeSageMath 2 agree
Crosswalk	SageMathOscar

Implementation

mappedoscarpackages/oracle/src/mappings.ts

mappedsagepackages/oracle/src/mappings.ts

mappedwolframpackages/oracle/src/mappings.ts

Wolfram has no direct product of permutation groups; the second factor's points are shifted past the first's, so the two act on disjoint points. Elements carry no a/b labels there, so only order, abelian-ness and class counts compare.