{ localUrl: '../page/5jh.html', arbitalUrl: 'https://arbital.com/p/5jh', rawJsonUrl: '../raw/5jh.json', likeableId: '3173', likeableType: 'page', myLikeValue: '0', likeCount: '1', dislikeCount: '0', likeScore: '1', individualLikes: [ 'PatrickStevens' ], pageId: '5jh', edit: '1', editSummary: '', prevEdit: '0', currentEdit: '1', wasPublished: 'true', type: 'comment', title: '"Are all the words in the free group, or just th..."', clickbait: '', textLength: '401', alias: '5jh', externalUrl: '', sortChildrenBy: 'recentFirst', hasVote: 'false', voteType: '', votesAnonymous: 'false', editCreatorId: 'EricRogstad', editCreatedAt: '2016-07-22 21:38:52', pageCreatorId: 'EricRogstad', pageCreatedAt: '2016-07-22 21:38:52', seeDomainId: '0', editDomainId: 'AlexeiAndreev', submitToDomainId: '0', isAutosave: 'false', isSnapshot: 'false', isLiveEdit: 'true', isMinorEdit: 'false', indirectTeacher: 'false', todoCount: '0', isEditorComment: 'true', isApprovedComment: 'true', isResolved: 'false', snapshotText: '', anchorContext: 'We can use the freely reduced words to construct the free group on a given set $X$; this group has as its elements the words over $X \\cup X^{-1}$, and as its group operation "concatenation followed by free reduction" \\(that is, removal of pairs $r r^{-1}$ and $r^{-1} r$\\)\\.\nThe notion of "freely reduced" basically tells us that $r r^{-1}$ is the identity for every letter $r \\in X$, as is $r^{-1} r$; this cancellation of inverses is a property we very much want out of a group\\.', anchorText: 'this group has as its elements the words', anchorOffset: '84', mergedInto: '', isDeleted: 'false', viewCount: '28', text: 'Are all the words in the free group, or just the freely-reduced words?\n\nIf the latter, does saying that the group operation involves free reduction imply that only freely-reduced words will end up in the free group? Because, by default I would assume that "the group has as its element the words over $X \\cup X^{-1}$" means that all the words (including non-freely-reduced ones) are in the free group.', metaText: '', isTextLoaded: 'true', isSubscribedToDiscussion: 'false', isSubscribedToUser: 'false', isSubscribedAsMaintainer: 'false', discussionSubscriberCount: '2', maintainerCount: '2', userSubscriberCount: '0', lastVisit: '', hasDraft: 'false', votes: [], voteSummary: 'null', muVoteSummary: '0', voteScaling: '0', currentUserVote: '-2', voteCount: '0', lockedVoteType: '', maxEditEver: '0', redLinkCount: '0', lockedBy: '', lockedUntil: '', nextPageId: '', prevPageId: '', usedAsMastery: 'false', proposalEditNum: '0', permissions: { edit: { has: 'false', reason: 'You don't have domain permission to edit this page' }, proposeEdit: { has: 'true', reason: '' }, delete: { has: 'false', reason: 'You don't have domain permission to delete this page' }, comment: { has: 'false', reason: 'You can't comment in this domain because you are not a member' }, proposeComment: { has: 'true', reason: '' } }, summaries: {}, creatorIds: [ 'EricRogstad' ], childIds: [], parentIds: [ 'freely_reduced_word' ], commentIds: [ '5jk', '5jl', '5jn', '5kb', '5kf' ], questionIds: [], tagIds: [], relatedIds: [], markIds: [], explanations: [], learnMore: [], requirements: [], subjects: [], lenses: [], lensParentId: '', pathPages: [], learnMoreTaughtMap: {}, learnMoreCoveredMap: {}, learnMoreRequiredMap: {}, editHistory: {}, domainSubmissions: {}, answers: [], answerCount: '0', commentCount: '0', newCommentCount: '0', linkedMarkCount: '0', changeLogs: [ { likeableId: '0', likeableType: 'changeLog', myLikeValue: '0', likeCount: '0', dislikeCount: '0', likeScore: '0', individualLikes: [], id: '17344', pageId: '5jh', userId: 'EricRogstad', edit: '1', type: 'newEdit', createdAt: '2016-07-22 21:38:52', auxPageId: '', oldSettingsValue: '', newSettingsValue: '' } ], feedSubmissions: [], searchStrings: {}, hasChildren: 'false', hasParents: 'true', redAliases: {}, improvementTagIds: [], nonMetaTagIds: [], todos: [], slowDownMap: 'null', speedUpMap: 'null', arcPageIds: 'null', contentRequests: {} }