1. A computer program product for performing processing associated with transactional execution in a computing environment, the computer program product comprising: a computer readable storage medium readable by a processing circuit and storing program instructions for execution by the processing circuit for performing a method comprising: executing a plurality of transaction begin instructions to initiate a plurality of transactions, the plurality of transactions creating a nest of transactions; obtaining, by a processor, an instruction to be executed as part of a transaction of the nest of transactions; computing one or more effective controls from one or more controls set by the plurality of transaction begin instructions, the one or more effective controls indicating whether one or more particular types of instructions, as indicated by the one or more effective controls, are permitted to be executed, wherein the one or more effective controls comprises an effective allow access register modification control that indicates whether an access register is permitted to be modified, and wherein the computing comprises determining a value for the effective allow access register modification control, wherein the determining the value for the effective allow access register modification control comprises performing a logical AND of the allow access register modification controls of the plurality of transaction begin instructions; allow access register modification controls of the plurality of transaction begin instructions; determining by the processor whether the instruction is a selectively restricted instruction that is prohibited from execution within the transaction, the determining being based on the computed one or more effective controls; and performing processing associated with the instruction based on whether the instruction is selectively restricted.