GroupElementQ
GroupElementQ[group,g]
returns True if the object g is an element of group and False otherwise.
Details
- GroupElementQ works with PermutationGroup objects and named groups.
Examples
open all close allBasic Examples (2)
Test membership of a permutation:
GroupElementQ[PermutationGroup[{Cycles[{{1, 3}, {6, 7}}], Cycles[{{3, 7}}]}], Cycles[{{1, 6}}]]The identity is an element of any group:
GroupElementQ[PermutationGroup[{Cycles[{{1, 3}, {6, 7}}], Cycles[{{3, 7}}]}], Cycles[{}]]Scope (1)
This is a subgroup of order 240 of 
:
group = PermutationGroup[{Cycles[{{1, 3, 2, 4}, {6, 7}}], Cycles[{{4, 5}}]}]GroupOrder[group]This permutation is not an element of the group:
GroupElementQ[group, Cycles[{{1, 4, 2, 3}, {5, 6, 7}}]]This permutation does belong to the group:
GroupElementQ[group, Cycles[{{1, 2, 4}, {3, 5}, {6, 7}}]]Text
Wolfram Research (2010), GroupElementQ, Wolfram Language function, https://reference.wolfram.com/language/ref/GroupElementQ.html.
CMS
Wolfram Language. 2010. "GroupElementQ." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/GroupElementQ.html.
APA
Wolfram Language. (2010). GroupElementQ. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/GroupElementQ.html