1. A computer program product for use by a transaction program 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 computer program product comprising: a tangible storage medium readable by a processing circuit and storing instructions for execution by the processing circuit for performing a method comprising: executing a string of instructions to complete a transaction of the first thread, beginning with one instruction of the string of instructions; determining whether the one instruction is part of an active atomic instruction group (AIG) of instructions associated with the transaction of the first thread; based on determining that the one instruction is part of the active AIG, determining whether a private-to-transaction (PTRAN) bit associated with an address of the one instruction in a main memory of a computing system is set, the PTRAN bit being located in the main memory, the main memory comprising a plurality of memory increments, and each of the plurality of memory increments having a respective directly addressable PTRAN bit in the main memory; based on determining that the PTRAN bit associated with the address of the one instruction in the main memory is not set: setting the PTRAN bit of the address associated with the one instruction in the main memory; adding a new entry to a cache structure and a transaction table, which together provide for entries in an active mode for the AIG, for the one instruction, the new entry including an old data state of the address of the one instruction stored in the cache structure and control information stored in the transaction table, wherein all addresses inspected or modified by instructions of the active AIG remain pending until the computing system indicates that the storage locations should be committed; and completing the one instruction as part of the active AIG; and executing the one instruction under a normal execution mode based on determining that the one instruction is not part of an active AIG.