1. A method for use by a transaction program on a computing system for managing memory access to a shared memory location for transaction data of a first thread, the shared memory location being accessible by the first thread and a second, thread, the method comprising: executing a string of instructions to complete a transaction of said first thread, beginning with one instruction of said string of instructions, and determining whether said one instruction is part of an active atomic instruction group (AIG) of instructions associated with said transaction of said first thread, if said one instruction is part of an active AIG, locating a transaction table which provides for entries in an active mode for said AIG wherein all storage locations inspected or modified by instructions of said active AIG remain pending until the computing system, indicates that the storage locations should be committed, and if said one instruction is not part of an active AIG, then executing a next instruction under normal execution mode.