The Financial Industry Regulatory Authority, or Finra, said it censured and fined Trillium Brokerage Services of New York and 11 of its employees for improprieties tied to so-called high-frequency trading. The violations took place over a three-month period at the end of 2006 and the start of 2007.

All told, the group paid $2.3 million in sanctions, the regulator said. The firm and the individuals didn’t admit to or deny the watchdog’s allegations.

Finra said Trillium, two execs and nine traders fabricated “market moving orders” that induced others to buy or sell at prices that were advantageous for Trillium.

Once their own orders to buy or sell against this fictitious market were filled, the Trillium traders withdrew the phony orders, the self-regulatory body said. The Trillium traders pulled this scam more than 46,000 times, Finra said, reaping $525,000 in profits, which they now are ordered to give back.

“Trillium’s trading conduct was designed to improperly bait unsuspecting market participants into executing trades at illegitimately high or low prices for the advantage of Trillium’s traders,” said Finra’s Thomas R. Gira. “Finra will continue to aggressively pursue disciplinary action for illegal conduct, including abusive momentum ignition strategies and high frequency trading activity that inappropriately undermines legitimate trading activity, in addition to related supervisory failures.”

The fine comes as the Securities and Exchange Commission is investigating the causes of the May 6 flash crash, in which shares of dozens of big companies plunged for a brief spell in the afternoon before recovering. Investors who had entered market orders for some stocks ended up selling the shares at prices well below the market’s trading range for the rest of the day.

In the most notorious case, shares of Accenture plunged as low as a penny from around $42 before recovering. Those trades were wiped out, but not before confidence in Wall Street took another hit.

Many observers blamed the crash on the rise of high-frequency trading, in which computers place trades by the thousands and withdraw many of them. Computerized trading has been accounting for a growing proportion of the market, and the flash crash suggested to many skeptics that high-frequency traders have been profiting at the expense of Mom and Pop types without providing any actual benefit to the market.

SEC chief Mary Schapiro said last week that the agency is investigating the crash and what brought it on, including high-frequency trading strategies and rapid order cancellations.

We know that, in the ordinary course, many high frequency trading firms cancel 90 percent or more of the orders they submit to the markets. There may, of course, be justifiable explanations for many cancelled orders to reflect changing market conditions.

The SEC and other regulators are looking carefully at certain practices in this area to assess whether they violate existing rules against fraudulent or other improper behavior.

But we also must understand the impact this activity has on price discovery, capital formation and the capital markets more generally, and consider whether additional steps such as registration and trading requirements are needed to ensure that these and other practices are used only in ways that foster — not undermine — fair and orderly markets.

Regulators have stepped up their efforts lately, but some skeptics of high-frequency trading have been warning since before the flash crash that the markets are rife with malfeasance and must be cleaned up. Sen. Ted Kaufman, D-Del., made this comment in a speech in April:

But in my view we have a “wild west” trading environment in equities, options and other markets where algorithms are battling algorithms, with no transparency or understanding at the SEC.  The SEC therefore has no ability to detect and police manipulative strategies. It’s not enough to rely on agency brokers to protect customer orders.  We need surveillance and enforcement for investors to have confidence.

Monday’s action is a start, though few skeptics of high-frequency trading are likely to be soothed by news of a three-year-old case.