E-Trade Group Inc. has found a merger match that will enable it to test on the Internet the "one-stop shop" proposition that has been hotly debated in conventional banking and financial services.

The on-line brokerage pioneer announced a definitive agreement Tuesday to buy Telebanc Financial Corp. of Arlington, Va., for $1.8 billion of stock. E-Trade said it will create the first "pure play," full-service banking and brokerage enterprise on the Internet.

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