Magma will compute an internal pc-presentation which will be used for internal computation, but the user's presentation will be used for all input and output. The recommended way to access the conditioned internal presentation is via the intrinsic ConditionedGroup.

Subsections

• Structure Operations
• Element Operations

The internally used, conditioned presentation of the pc-group G.

True if G has a conditioned presentation, false otherwise.

Given an element x of a pc-group G with n pc-generators and a conditioned presentation, where x is of the form a_1^(alpha_1) ... a_n^(alpha_n), return a_i^(alpha_i) for the smallest i such that alpha_i > 0. If x is the identity of G, then the identity is returned.

Given an element x of a pc-group G with n pc-generators and a conditioned presentation, where x is of the form a_1^(alpha_1) ... a_n^(alpha_n), return a_i for the smallest i such that alpha_i > 0. If x is the identity of G, then the identity is returned.

Given an element x of a pc-group G with n pc-generators and a conditioned presentation, where x is of the form a_1^(alpha_1) ... a_n^(alpha_n), return alpha_i for the smallest i such that alpha_i > 0. If x is the identity of G, then 0 is returned.

Given an element x of a pc-group G with n pc-generators and a conditioned presentation, where x is of the form a_1^(alpha_1) ... a_n^(alpha_n), return the smallest i such that alpha_i > 0. If x is the identity of G, then 0 is returned.

WeightClass(x) : GrpPCElt -> RngIntElt

The weight class of the element x. The WeightClass of an arbitrary element of a pc-group G is defined to be k if x in G_(delta_(k - 1)) and x notin G_(delta_(k)). If x is the identity of G, then WeightClass returns n + 1.

A sequence [p_1, ..., p_n] containing the primes associated with the pc-generators of G. The i-th term of the sequence contains the prime associated with generator a_i of G for i = 1, ..., n.

Eltseq(x) : GrpPCElt -> [RngIntElt]

Given an element x of a pc-group G, where x = a_1^(alpha_1) ... a_n^(alpha_n), 0 <= alpha_i < p_i for i = 1, ..., n, return the sequence Q of n integers defined by Q[i] = (alpha_i), for i = 1, ..., n.