Mr. Perdue, who badly trails Gov. Brian Kemp in the Republican primary for governor, accused Ms. Abrams of “demeaning her own race” in describing the state’s problems.
In primaries so far, Republican voters have appeared willing to nominate proponents of Donald Trump’s election falsehoods, making clear that this year’s races may well affect future elections.
The day’s biggest race, the Republican Senate primary in Pennsylvania, was too close to call. But elsewhere, candidates who dispute the 2020 outcome ran away with G.O.P. contests.
Mr. Mastriano, a retired Army colonel, prevailed over a last-ditch effort by his rivals and state Republican leaders to stop him out of the fear he will be a weak general-election candidate.
In the first lawsuit of its kind, two real Electoral College delegates from 2020 are seeking damages from 10 fake ones who tried to help Donald Trump overturn his defeat in the state.
Mr. Mastriano, who has promoted many false claims of a stolen 2020 election, was the leading Republican candidate for governor even before Donald Trump’s endorsement.
Mr. Pillen, a University of Nebraska regent backed by the state’s departing governor, won a tight three-way race that included a scandal-plagued candidate endorsed by Donald Trump.
Charles W. Herbster’s bid for governor has set off a bitter fight for power in a state once known for its genteel politics.
Charles W. Herbster, who has been endorsed by Donald Trump for Nebraska governor, was accused of groping a second woman at a 2019 Republican fund-raising event. He denies both allegations.
Republicans in several states are trying to oust conservative governors by harnessing anti-establishment energy. But in battles for a state’s top job, it’s hard to beat the establishment.