A federal magistrate last week refused to issue an injunction to halt construction of the 3.2-mile extension of the Red Line subway, indicating that a suit to stop construction until a new Environmental Impact Statement (EIS) is written will fail.

A group called Red Line Alert, composed of businessmen and homeowners who are affected by the construction, is trying to stop the extension on the grounds that the original 1500-page EIS does not adequately warn those affected by the ramifications of the extension.

U.S. Magistrate Laurence Cohen defended the original EIS in a 31-page opinion to U.S. District Court Judge David Nelson, and said the allegations of Red Line Alert are "frivolous" and, in one case, "simply inaccurate."

The Red Line Alert is a coalition of the North Cambridge Planning Team, the Mystic River Watershed Associwtion, and the Harvard-Porter Square Alert, a group of businesses on Mass Ave.

The Cambridge City Council supported the injunction by a vote of six to three, despite a warning from the director of the Massachusetts Bay Transit Authority (MBTA), the group in charge of the extension, that the delay caused by an injunction might kill the entire project.

City officials said this week that in light of Cohen's refusal to issue an injunction, the city would not pursue the matter further. The City Council has already given $10,000 to a leading New England environmental lawyer and is expected to approve $19,000 more at tonight's council meeting.

"The EIS,"Cohen wrote, "was sufficient in its scope and detail to provide the Administrator with sufficient facts to make an 'eyes open' judgment whether or not to fund the project, even though the EIS, because of its sheer scope, could not detail with more precision upon whose block each phase of construction might fall, or every possible methodology of construction which might be needed to complete the project."

Cohen noted that the major argument proferred by Red Line Alert-that the original EIS was written before Alewife was designated as a location for the final station-made no major difference on the impact of the extension on the environment, especially considering a further extension to the originally designated Arlington Heights is still likely in the future