1. A method of controlling execution of instructions within transactions of a computing environment, said method comprising: obtaining, by a processor, a machine instruction for execution, the machine instruction being defined for computer execution according to a computer architecture, the machine instruction comprising: an operation code to specify a transaction begin operation; and at least one control to be used in controlling execution of one or more types of instructions in transactional processing; executing, by the processor, the machine instruction, the executing comprising: initiating a transaction; and using a first control of the at least one control of the machine instruction to determine a first value, the first value to control execution within the transaction of an instruction of a first type, wherein the first control is an allow access register modification control, and wherein based on the first control being the allow access register modification control, the first type comprises instructions that modify one or more access registers, the allow access register modification control to be used to indicate whether the transaction is permitted to execute an instruction that modifies an access register that includes an indirect specification of an address space control element to be used in address translation; and controlling execution of a particular instruction of the transactional processing based on the first value, the first value determined using the allow access register modification control.