She listened intently each time the topic was brought up, but calmly but firmly cast aside any suggestion that her appointment was historic for the male-dominated industry.
"There has been a lot of coverage," she said. "But my gender doesn't really factor into my thinking as I come into a room."
She did pledge to be a visible, approachable presence throughout the company —again a contrast to the imperial leaders G.M. has had in the past — holding regular town-hall meetings, smaller get-acquainted sessions and web chats with employees. This weekend, Ms. Barra will travel to Europe for the first of several planned visits to G.M.'s regional operations.
Mr.Cole, whose father was president of G.M. in the 1960s, said employees at the company seemed keenly optimistic to have someone at the helm whom many of them have known personally for years.
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"It's going to be an altogether different situation than with Akerson, who was more of a brusque, top-down kind of manager," he said. "Mary just has a far deeper understanding of the company and its strengths and weaknesses."
Ms.Barra is publicly reinforcing two of G.M.'s most ambitious goals — achieving 10 percent pretax profit margins in North America by mid decade, and steering the troubled European unit to a break-even performance in the time period.
To achieve those targets, she will need to step up the cadence of new products. At the Detroit show, G.M. showed off two vehicles, the new GMC Canyon midsize pickup and the Cadillac ATScoupe, that it hopes will generate steady sales gains.
Industry analysts are, for the most part, confident that G.M. has turned a corner in its effort to improve quality in its vehicles and add sizzle with striking designs and the latest technology.
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"G.M. cars just look better than they have in a long, long time," said Joseph Phillippi, an executive with the marketing firm Auto Trends. "Something like the ATS coupe is an attractive alternative to even the best of the German luxury models."
Ms.Barra's star turn at the Detroit auto show underscored the amount of good will she has already engendered for G.M.
A high point was her tour of the Chevrolet brand exhibit with Vice President Joseph R. Biden Jr., who could not stop admiring the sleek new, yellow Corvette on the stand.
But she could not help but reflect on Thursday about the same auto show five years ago, when G.M. employees collectively held their breath, hoping that the Obama administration would bail out the company with federal funds.
"I'm a person who looks at the glass as half-full," she said. "I also believe if you have a problem you better solve it. Because if you don't solve it, you won't be here or the company won't be here."
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