1. A method of controlling execution of instructions within transactions of a computing environment, a transaction effectively delaying committing transactional stores to main memory until completion of a selected transaction, 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; and executing, by the processor, the machine instruction, the executing comprising: initiating a transaction; and using a first control of the at least one control 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 one of an allow access register modification control or an allow floatin point operation control, and wherein based on the first control being the allow access register modification control, the first type comprises instructions that modify a type of register referred to as an access register, the access register including an indirect specification of an address space control element to be used in address translation, 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; and based on the first control being the allow floating point operation control, the first type comprises specified floating point instructions, the allow floating point operation control to be used to indicate whether the transaction is permitted to execute the specified floating point instructions.