IEX currently operates as a private exchange, or dark pool, but has less than 2 percent of the market. In order to challenge Wall Street heavyweights such as the New York Stock Exchange and Nasdaq, it needed to become a registered exchange. The Securities and Exchange Commission approved its application to make that conversion late Friday.

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“Today’s actions promote competition and innovation, which our equity markets depend on to continue to deliver robust, efficient service to both retail and institutional investors,” said Mary Jo White, chair of the Securities and Exchange Commission.

The firm was thrown into the spotlight after being featured in Michael Lewis’s 2014 book “Flash Boys: A Wall Street Revolt,” which argued that the markets are rigged against mom-and-pop investors.

But the company’s application attracted high-profile detractors, including the New York Stock Exchange and Nasdaq, who say the start-up would add unnecessary complexity to the financial system and was asking for special treatment.

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At the center of the debate is the value of 350 microseconds. That is how long IEX would delay every order to buy or sell a stock. IEX says the speed bump prevents high-speed traders from cutting the line to pick up stocks at the best prices, leaving slower mom-and-pop traders in the dust.

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But critics say the delay breaks a central covenant of the financial system: Exchanges should always show the best price available for a stock. Any delay, even a microscopic one, is problematic, they say.

“We expect brokers, who are required to get the best deal for their clients, will be watching IEX closely to monitor the quality of their trading execution,” said Bill Harts, chief executive of Modern Markets Initiative, which promotes high-frequency trading firms.

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The debate surrounding IEX threw a spotlight on the technological changes that have transformed Wall Street. Stock exchanges once dominated by screaming brokers, scrambling to get the best price on a stock, have been taken over by computers and traders using complex algorithms to find an advantage — measured in fractions of a second.