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Business Combinations - Additional Information (Detail) - USD ($)			9 Months Ended		12 Months Ended
	Jul. 26, 2021	Oct. 01, 2019	Sep. 30, 2021	Sep. 30, 2020	Dec. 31, 2020
Cash payment			$ 51,000,000	$ 6,000,000
2021 Acquisitions [Member]
Purchase price consideration transferred			68,000,000
Cash paid at closing			51,000,000
Net revenues from acquisition			9,000,000
Cash payment			4,000,000
Business combination accrued consideration			13,000,000
Goodwill, expected tax deduction			21,000,000
2021 Acquisitions [Member] | Maximum [Member]
Operating income (loss) from acquisition			1,000,000
2020 Acquisitions [Member]
Cash paid at closing					$ 329,000,000
Net of cash acquired and accrued consideration					5,000,000
Goodwill, expected tax deduction					20,000,000
2020 Acquisitions [Member] | Safety Services [Member]
Purchase price consideration transferred					324,000,000
Cash payment					319,000,000
Business combination accrued consideration					$ 5,000,000
2020 Acquisitions [Member] | Safety Services [Member] | Minimum [Member]
Business combination accrued consideration paid out period					1 year
APi Acquisition [Member]
Contingent compensation			13,000,000		$ 39,000,000
Maximum payout of contingent compensation			49,000,000		85,000,000
Payout of accrued contingent compensation			13,000,000		39,000,000
Liability for deferred payments			$ 13,000,000		$ 16,000,000
APi Acquisition [Member] | Minimum [Member]
Contingent compensation arrangements recognized period		3 years
Liability for deferred payments recognition period		12 months
APi Acquisition [Member] | Maximum [Member]
Contingent compensation arrangements recognized period		5 years
Liability for deferred payments recognition period		24 months
Chubb Limited Fire and Security Business [Member]
Purchase price consideration transferred	$ 3,100,000,000
Cash acquired	2,900,000,000
Assumed liabilities, and other adjustments	$ 200,000,000

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The amount of goodwill arising from a business combination that is expected to be deductible for tax purposes.

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Amount of consideration transferred, consisting of acquisition-date fair value of assets transferred by the acquirer, liabilities incurred by the acquirer, and equity interest issued by the acquirer.

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Amount of liabilities incurred by the acquirer as part of consideration transferred in a business combination.

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The cash inflow associated with the acquisition of business during the period (for example, cash that was held by the acquired business).

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