The phrase "act faithfully" is correct and usable in written English.
It can be used in contexts where one is expected to perform duties or responsibilities with integrity and loyalty.
Example: "As a member of this organization, you are expected to act faithfully in all your dealings with clients and colleagues."
Alternatives: "perform with integrity" or "serve loyally".
Did he act faithfully when his Attorney General decided not to prosecute marijuana offences in states where such activity is no longer criminal under state law?
The Lord taught me to be faithful, in all things, and to act faithfully two ways; viz., inwardly to God, and outwardly to man".
You act faithfully regardless of whether or not your firmly held convictions are popular with the government, because if you don't (fun fact), they're not actually firmly held convictions they're merely propaganda, useful for whipping the theologically unsophisticated into a frenzy.
Whether courts decline to adjudicate whether the Congress has acted pretextually is not to affirm that it has acted faithfully.
This is equivalent to showing that any locally compact topological group that acts faithfully on a connected 3-manifold has to be a Lie Group.
Note that the wreath recursion is usually not an isomorphism (but is an embedding, since we assume that G acts faithfully on (X^*)).
The group of translations acting in Ω (which has periodic boundaries) is the torus (mathbb {R}^{2}/mathbb {Z}^{2}), which, moreover, acts faithfully on any (V_{0}) with square or hexagonal pattern.
The absolute Galois group (Gal(bar{{mathbb {Q}}} /{mathbb {Q}})) acts faithfully on the set of irreducible components of the Gieseker moduli space of surfaces of general type, begin{aligned} mathfrak M : = cup _{x,y in {mathbb {N}}, x,y ge 1} mathfrak M_{x,y}.
After an incomplete initial attempt in [28] in joint work with Ingrid Bauer and Fritz Grunewald, we were able in [29] to show: The absolute Galois group (Gal(bar{{mathbb {Q}}} /{mathbb {Q}})) acts faithfully on the set of connected components of the Gieseker moduli space of surfaces of general type, begin{aligned} mathfrak M : = cup _{x,y in {mathbb {N}}, x,y ge 1} mathfrak M_{x,y}.
I followed this exercise routine faithfully.
There followed a new disco recording of Sisters, appearances at gay pride events and a national tour with the Syd Lawrence Orchestra, in which the 50s stage act was faithfully recreated, causing one reviewer to remark that "the time-warp element is uncanny".
